# Let a=i-k, b=xi+j+(1-x)k and c=yi+xj+(a+x+y)k. Then [a b c] depends on

1.  only y

2.  only x

3.  both x and y

4.  neither x nor y

4

neither x nor y

Explanation :
No Explanation available for this question

# The vectors a+2b+3c, 2a+b-2c, 3a-7c are

1.  coplanar

2.  collinear

3.  non-coplanar

4.  none

4

coplanar

Explanation :
No Explanation available for this question

# The points 2a+3b-c, a-2b+3c, 3a+4b-2c, a-6b+6c are

1.  collinear

2.  coplanar

3.  non-coplanar

4.  none

4

coplanar

Explanation :
No Explanation available for this question

# The vectors i-2j+3k, 2i-3j+4k, i-3j+5k are

1.  collinear

2.  coplanar

3.  non-coplanar

4.  none

4

coplanar

Explanation :
No Explanation available for this question

# The vector 5i+6j+7k, 7i-8j+9k, 3i+20j+5k are

1.  coplanar

2.  collinear

3.  non-coplanar

4.  none

4

coplanar

Explanation :
No Explanation available for this question

# The points (2, 1, -1), (1, 1, 1), (2, 2, 1), (0, 2, 5) are

1.  coplanar

2.  collinear

3.  non-coplanar

4.  none

4

coplanar

Explanation :
No Explanation available for this question

# The condition that the lines r=a+tb, r=c+sd to intersect each other is

1.  [c-a b d]=0

2.  [b-d a c ]=0

3.  [a-b c d]=0

4.  [c-d a b]=0

4

[c-a b d]=0

Explanation :
No Explanation available for this question

# The vector equation of the plane containing line r=a+tb and parallel to the line r=c+sd is

1.  [r-a b d]=0

2.  [r-b c d]=0

3.  [r-d a b]=0

4.  none

4

[r-a b d]=0

Explanation :
No Explanation available for this question

# The vector equation of the plane through the points a, b and paralle to the line r=c+td is

1.  [r b-a d]=[a b c]

2.  [r b-a d]=[a b t]

3.  [r b-c a]=[a b d]

4.  [r c-a b]=[a c d]

4

[r b-a d]=[a b t]

Explanation :
No Explanation available for this question

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

1.  [r-(i+j+k) 2i+3j-k i+2j+3k]=0

2.  [r 2i+3j-k i+2j+3k]=0

3.  [r-(i+j+k) i+2j-2k  j+2k]=0

4.  [r  i+2j-2j-k  j+2k]=0

4