- If , ⃗^ are two unit vectors and Ѳ is
the angle between them, then the value
of cos^ is equal to:
(a)^ | ⃗^ | (b)^ | ⃗^ | (c) |^ ⃗^
⃗ (^) |
| ⃗ || ⃗^ |^ (d)
|^
⃗ (^) |
17. If | |= 3, | ⃗^ |= 4 and | ⃗^ |= 5, then
the value of | ⃗^ | is equal to:
(a) 6 (b) 5√ (c) 5 (d) 4
18. The area of the parallelogram with
= ̂ ̂ ̂ and ⃗^ = ̂ ̂ ̂ as
consecutive sides, is equal to:
(a) √ sq units (b) 2√ sq units (c)
2 √ sq units (d) √ sq units
19. The position vectors of P, Q, R and S
are ̂ ̂ ̂ ̂ ̂ ̂ ̂ ̂ and
̂ ̂ ̂ respectively, then which one
of the following forms a parallel pairs?
(a) ⃗⃗⃗⃗⃗^ and ⃗⃗⃗⃗⃗^ (b) ⃗⃗⃗⃗⃗^ and ⃗⃗⃗⃗⃗^ (c) ⃗⃗⃗⃗⃗^
and ⃗⃗⃗⃗⃗^
(d) none of these
20. For any three vectors , ⃗^ and ,
( ⃗^ ) ⃗^ ( ) ( ⃗^ )
is equal to:
(a) 2[( ⃗^ ) ( ⃗^ ) ( )] (b) -
2 [( ⃗^ ) ( ⃗^ ) ( )] (c) ⃗^
(d) [( ⃗^ ) ( ⃗^ ) ( )]
21. If | ⃗^ | | ⃗^ |, then:
(a) is parallel to ⃗^ (b) is
perpendicular to ⃗^ (c) | | = | ⃗^ | (d)
none of these
22. If ( ⃗^ ).( ⃗^ )= 0, then:
(a) and ⃗^ are perpendicular (b) and
⃗^ are parallel (c) | | | ⃗^ | (d) ⃗^
23. If ⃗^ is perpendicular to ,
where ̂ ̂ ̂, ⃗^ ̂ ̂
̂ and ̂ ̂, then t is equal to:
(a) 4 (b) 5 (c) 6 (d) 7
24. If ̂ ̂ ̂, where
are scalar quantities and ̂ ̂ ̂
are unit vectors in three mutually
perpendicular directions, then
| ̂|^ | ̂|^ is equal to:
(a) (b) (c)
2 (d)
25. If | ⃗^ |
| ⃗^ |
and
| | then ) | ⃗^ | is equal to:
(a) 3 (b) 8 (c) 12 (d) 16
26 .The position vector of points A, B, C,
D are ⃗^ ⃗^ and ⃗^
respectively. The vector ⃗⃗⃗⃗⃗^ is:
(a) ⃗^ (b) 3 ⃗^ (c) ⃗^ (d) -
⃗^
27. If P is a point on the circumference
of a semicircle of radius a being
bounded by the diameter BC, then
which one of the following is correct?
(a) ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ (b) ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ (c)
⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^ (d) ⃗⃗⃗⃗⃗^ ⃗⃗⃗⃗⃗^
28. The sine of the angle between
vectors ̂ ̂ ̂ and
⃗^ ̂ ̂ ̂ is equal to:
(a) √^ (b) (c) (d) √^