Eamcet - Maths - Vector Algebra

Observe the following statements : A : Three vectors are coplanar if one of them is expressible as a linear combination ofthe other two. R : Any three coplanar vectors are linearly dependent.Then which of the following is true

A.  Both A and R are true and R is the correct explanation of A

B.  Both A and R are true but R is not the correct explanation of A

C.  A is true, but R is false

D.  A is false, but R is true

View Answer  

Correct Answer :

Both A and R are true but R is not the correct explanation of A



Explanation :
No Explanation available for this question

If |a+b|2=|a|2+|b|2 then the angle between a and b is

A.  900

B.  600

C.  450

D.  1200

View Answer  

Correct Answer :

900



Explanation :
No Explanation available for this question

A: Angle between the vector i-2j+k, 2i-j-k is π/3 R: If θ is  the angle between a, b then cosθ=a.b/|a||b|

A.  Both A and R are true and R is the correct explanation of A

B.  Both A and R are true but R is not correct explanation of A

C.  A is true R false

D.  A is false but R is true

View Answer  

Correct Answer :

Both A and R are true and R is the correct explanation of A



Explanation :
No Explanation available for this question

If p=(2, 1, 3), q=(-2, 3, 1), r=(3, -2, 4) and j is the unit vector in the direction of y-axis then (2p+3q-4r). j=

A.  18

B.  19

C.  20

D.  21

View Answer  

Correct Answer :

19



Explanation :
No Explanation available for this question

If three points A, B, C have position vectors (1, x, 3) and (y, -2, -5) respectively and if they are collinear, then (x, y)=

A.  (2, -3)

B.  (-2, 3)

C.  (-2,-3)

D.  (2, 3)

View Answer  

Correct Answer :

(2, -3)



Explanation :
No Explanation available for this question

I: If the vectors a=(1, x, -2), b=(x, 3, -4) are mutually perpendicular,then x=2 II: If a=i+2j+3k, b=-i+2j+k, c=3i+j and a+tb is perpendicular to c then t=5

A.  Only I is true

B.  Only II is true

C.  both I and II are true

D.  neither I nor II are true

View Answer  

Correct Answer :

Only II is true



Explanation :
No Explanation available for this question

If a=i+4j, b=2i-3j and c=5i+9j then c=

A.  2a+b

B.  a+2b

C.  a+3b

D.  3a+b

View Answer  

Correct Answer :

3a+b



Explanation :
No Explanation available for this question

The vector area of the triangle whose adjacent sides i-2j+2k, 3i+2j-5k is

A.  1/2(6i+11j-8k)

B.  1/2(6i-11j+8k)

C.  1/2(6i+11j+8k)

D.  1/2(6i-11j-8k)

View Answer  

Correct Answer :

1/2(6i+11j+8k)



Explanation :
No Explanation available for this question

The vector c directed along the internal bisector of the angle between the vectors 2i+3j-6k and -2i-j+2k with |c|=√21 is

A.  ±(-8i+2j-4k)

B.  ±(-4i+j-2k)

C.  ±(-12i+3j-6k)

D.  none

View Answer  

Correct Answer :

±(-4i+j-2k)



Explanation :
No Explanation available for this question

The vector equation of the plane passing through the point 2i+2j-3k and parallel to the vectors 3i+3j-5k, i+2j+k is

A.  r=s(2i+j-k)+t(i+2j+2k)

B.  r=2i+2j-3k+s(3i+3j-5k)+t(i+2j+k)

C.  r=(i+2j+3k)+s(-2i+3j+k)+t(2i-3j+4k)

D.  none

View Answer  

Correct Answer :

r=2i+2j-3k+s(3i+3j-5k)+t(i+2j+k)



Explanation :
No Explanation available for this question

A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is

A.  4i+3j-k /√26

B.  2i-6j-3k/7

C.  3i-2j+6k/7

D.  2i-3j-6k/7

View Answer  

Correct Answer :

3i-2j+6k/7



Explanation :
No Explanation available for this question

If a=(1, 1, 1), c=(0, 1, -1) are given vectors then a vector b sastisfying the equations axb=c and a.b=3 is

A.  5i+2j+2k

B.  5/2i+j+k

C.  5/3i+2/3j+2/3k

D.  i+2/5j+2/5k

View Answer  

Correct Answer :

5/3i+2/3j+2/3k



Explanation :
No Explanation available for this question

The magnitude of the projection of the vector a = 4i - 3j + 2k on the line which makes equal angles with the coordinate axes is

A.  √2

B.  √3

C.  1/√3

D.  1/√2

View Answer  

Correct Answer :

√3



Explanation :
No Explanation available for this question

If AB=2a+b and AD=a-2b where |a|=1, |b|=1 and (a, b)=600 are the adjacent sides of a parallelogram, then the length of the diagonal BD is

A.  √13

B.  √7

C.  √12

D.  none

View Answer  

Correct Answer :

√7



Explanation :
No Explanation available for this question

Arrange the magnitudes of following vectors in ascending order A) ixj+ jxk+kxi  B) If lal=2, lbl=3, (a, b)=450 then axb C) (2i-3j+2k)x(3i-j+4k)

A.  A, B, C

B.  C. B, A

C.  B, C, A

D.  B, A, C

View Answer  

Correct Answer :

A, B, C



Explanation :
No Explanation available for this question

The vector of magnitude √51 which makes equal angles with the vector a=1/3(i-2j+2k), b=1/5(-4i-3k), c=j is

A.  ±(i+2j-k)

B.  ±(2i+j-k)

C.  ±(5i-j-5k)

D.  none

View Answer  

Correct Answer :

±(5i-j-5k)



Explanation :
No Explanation available for this question

Statement I: The points 4i+5i+k, -j-k, 3i+9j+ 4k and -4i+4j+4k are coplanar Statement II  : The given points from  the  vertices of a parallelogram. Which of the following is true? a)  Both statements  are  true and statement II is correct explanation of statement I b)  Both  statements  are true  and statement II is not correct explanation of statement I cv) Statement I is true and statement II is false d)  Statement I is false and  Statement II is true

A.  Both statements  are  true and statement II is correct explanation of statement I

B.  Both  statements  are true  and statement II is not correct explanation of statement I

C.  Statement I is true and statement II is false

D.  Statement I is false and  Statement II is true

View Answer  

Correct Answer :

Statement I is true and statement II is false



Explanation :
No Explanation available for this question

If a is any vector then (axi)2+(axj)2+(axk)2=

A.  a2

B.  2a2

C.  3a2

D.  4a2

View Answer  

Correct Answer :

2a2



Explanation :
No Explanation available for this question

The vector area of the parallelogram whose diagonals are i+j-2k, 2i-j+2k is

A.  1/2(i+4j-3k)

B.  1/2(i-4j+3k)

C.  1/2(i+4j+3k)

D.  1/2(i-4j-3k)

View Answer  

Correct Answer :

1/2(i-4j-3k)



Explanation :
No Explanation available for this question

The area of the parallelogram whose diagonals are i-3j+2k, -i+2j is

A.  4√29 sq.unit

B.  1/2 √21 sq.unit

C.  10√3 sq.unit

D.  1/2√270 sq.unit

View Answer  

Correct Answer :

1/2 √21 sq.unit



Explanation :
No Explanation available for this question

(2i-3j+k).(i-j+2k)x(2i+j+k)=

A.  -12

B.  14

C.  10

D.  15

View Answer  

Correct Answer :

-12



Explanation :
No Explanation available for this question

Let v- = 2i- + j- - k- and u- = i- + 3k- . If u is any unit vector then the maximum value of the scalar triple product [u- v- w-] is

A.  1

B.  √10 + √6

C.  √59

D.  √60

View Answer  

Correct Answer :

√59



Explanation :
No Explanation available for this question

I: If a=3i-2j+k, b=2i-4j-3k, c=-i+2j+2k then a+b+c=4i-4j II: If a=i-j+2k, b=2i+3j+k, c=i-k, then magnitude of a+2b-3c is √78

A.  Only I is true

B.  Only II is true

C.  both I and II are true

D.  Neither I nor II are true

View Answer  

Correct Answer :

both I and II are true



Explanation :
No Explanation available for this question

If a=i+2j-3k, b=2i+j+k, c=i+3j-2k then (axb)x(bxc)=

A.  5(2i+j+k)

B.  -5(2i+j+k)

C.  10(2i+j+k)

D.  -10(2i+j+k)

View Answer  

Correct Answer :

-10(2i+j+k)



Explanation :
No Explanation available for this question

A: If a, b, c are vectors such that [a b c]=4 then [axb bxc cxa]=64 R: [axb bxc cxa]=[a b c]2

A.  Both A and R are true and R is the correct explanation of A

B.  Both A and R are true but R is not correct explanation of A

C.  A is true R false

D.  A is false but R is true

View Answer  

Correct Answer :

A is false but R is true



Explanation :
No Explanation available for this question

If a,b,c are three non-collinear points then r=(1-p-q)a+pb+qc represents

A.  line

B.  plane

C.  plane passing through origin

D.  sphere

View Answer  

Correct Answer :

plane



Explanation :
No Explanation available for this question

If a=i+j-2k , b=-i+2j+k, c=i-2j+2k then a unit vector parallel to a+b+c=

A.  2i+j+k/√6

B.  i+j+k/√3

C.  i-2j+k/√6

D.  i-j+k/√3

View Answer  

Correct Answer :

i+j+k/√3



Explanation :
No Explanation available for this question

The vectors (1, 2, 3), (4, 5, 6), (6, 7, 8) are

A.  Linearly dependent

B.  linearly independent

C.  collinear

D.  none

View Answer  

Correct Answer :

Linearly dependent



Explanation :
No Explanation available for this question

The relation between the vectors a+3b+4c, a-2b+3c, a+5b-2c, 6a+14b+4c is

A.  1(a+3b+4c)+2(a-2b+3c)+2(a+5b-2c)-1(6a+14b+4c)=0

B.  1(a+3b+4c)+2(a-2b+3c)+3(a+5b-2c)-2(6a+14b+4c)=0

C.  1(a+3b+4c)+2(a-2b+3c)+3(a+5b-2c)-1(6a+14b+4c)=0

D.  none

View Answer  

Correct Answer :

1(a+3b+4c)+2(a-2b+3c)+3(a+5b-2c)-1(6a+14b+4c)=0



Explanation :
No Explanation available for this question

The centre of the sphere (r-3i+3j+5k).(r+i-j+3k)=0 is

A.  (4, -6, 8)

B.  (2, -3, 4)

C.  (2, 2, 2)

D.  (1, 1, 1)

View Answer  

Correct Answer :

(1, 1, 1)



Explanation :
No Explanation available for this question