- If , ⃗^ and are position vectors of
points A, B and C in space, then area of
triangle ABC is equal to:
(a)^ | ⃗^ |
(b)^ | ⃗^ ⃗^ |
(c)^ | ⃗^ ⃗^ |
(d) | ⃗^ ⃗^ |
- If ⃗^ = 0 and | | | ⃗^ |
| | (^) √ , then angle between and ⃗^
is:
(a)^ (b)^ (c)^ (d)^
- If , ⃗^ and are unit vectors such
that ⃗^ = 0, then angle between
and ⃗^ is:
(a)^ (b)^ (c)^ (d) none of these
- If the vector ̂ ̂ ̂,
⃗^ ̂ ̂ ̂, ̂ ̂ ̂ are
three non-coplanar vectors and
|
|= 0, then the value of
abc is equal to:
(a) 2 (b) 1 (c) 0 (d) - 1
- If | |= | ⃗^ |= | ⃗^ |= 1, then the value
of | ⃗^ | is equal to:
(a) 1 (b) √ (c) √ (d) √
- If | | | ⃗^ | | | such that
( ⃗^ ), ⃗^ ( ) and ( + ⃗^ ),
then the value of | ⃗^ | is equal to:
(a) 5 (b) 7 (c) √ (d) √
- If in a right angled triangle ABC, the
hypotenuse AB= p, then the value of
⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ is equal to:
(a) 2 (b) (c)^ (d) p - If and ⃗^ are two unit vectors
inclined at an angle^ then the value of
| ⃗^ |, is:
(a) greater than 1 (b) less than 1 (c)
equal to 1 (d) equal to 0
13. A unit vector perpendicular to the
two vectors ̂ ̂ ̂ and 2 ̂ ̂ ̂
is equal to:
(a) 35(5 ̂ ̂ ̂) (b) √ (5 ̂ ̂
̂)
(c) √^ (5 ̂ ̂ ̂) (d) (5 ̂ ̂
̂)14. If , a vector of magnitude 50 is
collinear with the vector ⃗^ =
6 ̂ ̂ ̂ and makes an acute angle
with the positive direction of z-axis,
then the vector is equal to:
(a) 24 ̂ ̂ ̂ (b) - 24 ̂ ̂
̂
(c) 16 ̂ ̂ ̂ (d) - 12 ̂ ̂
̂15. If + ⃗^ and | | | ⃗^ |
and | | , then the value of
⃗^ ⃗^ is equal to:
(a) 100 (b) – 100 (c) 200 (d) – 200