# Let a=i+j+k, b=i-j+2k and c=xi+(x-2)j-k. If the vector c lies in the plane of a and b then x equals

1.  0

2.  1

3.  -4

4.  -2

4

-2

Explanation :
No Explanation available for this question

# If the vectors ai+j+k, i+bj+k, i+j+ck(a≠b≠c≠1) are coplanar, then the value of 1/1-a+1/1-b+1/1-c=

1.  0

2.  3

3.  2

4.  1

4

1

Explanation :
No Explanation available for this question

# Let a, b, c be the distinct non-negative numbers. If the vectors ai+aj+ck, i+k and ci+cj+bk lie in a plane then c is

1.  the arthematic mean of a and b

2.  the geometric mean of a and b

3.  the harmonic mean of a and b

4.  equal to zero

4

the harmonic mean of a and b

Explanation :
No Explanation available for this question

# If a=i+j+k, b=4i+3j+4k and c=i+αj+βk are linearly dependent vectors and |c|=√3 then

1.  α=1, β=-1

2.  α=1, β=±1

3.  α=-1, β=±1

4.  α=±1, β=1

4

α=±1, β=1

Explanation :
No Explanation available for this question

# If the volume of the parallelepiped whose edges are represented by 12i+λk, 3j-k, 2i+j-15k is 46 then λ=

1.  1

2.  2

3.  3

4.  4

4

3

Explanation :
No Explanation available for this question

# The value of k for which the points A(1, 0, 3), B(-1, 3, 4), C(1, 2, 1) and D(k, 2, 5) are coplanar is

1.  1

2.  2

3.  0

4.  -1

4

-1

Explanation :
No Explanation available for this question

# If the points 3i-2j-k, 2i+3j-4k, i+j+2k, 4i+5j+λk are coplanar then λ=

1.  12

2.  -94/7

3.  3/2

4.  5

4

-94/7

Explanation :
No Explanation available for this question

# If a, b, c, d are the position vectors of A, B, C, D respectively, then the volume of the tetrahedrone ABCD is

1.  ±1/6{[a b c]-[a b d]+[a c d]-[b c d]}

2.  {[a b c]-[a b d]+[a c d]-[b c d]}

3.  ±1/6{[b c a]-[c b a]+[a c d]-[b c d]}

4.  ±1/8{[b c a]-[a c d]+[a b d]-[b c d]}

4

±1/6{[a b c]-[a b d]+[a c d]-[b c d]}

Explanation :
No Explanation available for this question

# If d=x(axb)+y(bxc)+z(cxa) and [a b c]=1/8, then x+y+z=

1.  8d. (a+b+c)

2.  d. (a+b+c)

3.  4d. (a+b+c)

4.  none

4

8d. (a+b+c)

Explanation :
No Explanation available for this question

# If a, b, c are non-coplanar vectors and λ is real number then [λ(a+b) λ2b λc]=[a b+c b] for

1.  exactly one value of λ

2.  no value of λ

3.  exactly three values of λ

4.  exactly two values of λ

4