vector algebra one mark questions. choose the correct answer 1. if is a non-zero vector and m is a...
TRANSCRIPT
Vector Algebra One Mark Questions
PREPARED BY:R.RAJENDRAN. M.A., M. SC., M. ED.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21
Choose the Correct Answer
1. If is a non-zero vector and m is a non-zero scalar then m is a unit vector if
(a) m = 1 (b) a = |m|
(c) a = 1/|m| (d) a = 1
2. If and are two unit vectors and is the angle between them, then is a unit vector if
(a) (b)
(c) (d)
a a
a b ba
3
4
3
2 2
Choose the Correct Answer
3. If then
(a) u is a unit vector (b)
(c) (d)
4. If and include an angle 120 and their magnitude are 2 and 3, then is equal to
(a) 3 (b) – 3
(c) 2 (d) – 3/2
) b a ( c ) a c ( b ) c b ( au
cbau
a b ba
0 u 0 u
Choose the Correct Answer
5. If then the angle between and is
(a) /6 (b) 2/3
(c) 5/3 (d) /2
6. The vectors and are perpendicular when
(a) a = 2, b = 3, c = – 4 (b) a = 4, b = 4, c = 5
(c) a = 4, b = 4, c = – 5 (d) a = – 2 , b = 3, c = 4
5 c ,4 b ,3 a ,0 c b a
k 4 j 3 i 2
a b
k j i cba
Choose the Correct Answer
7. The area of the parallelogram having a diagonal and a side is
(a) 103 (b) 630
(c) 3/23 (d) 330
8. If then
(a) (b)
(c) (d)
k j i 3
baba
k 4 j 3 i
toparallel is ba lar toperpendicu is ba
ba rsunit vecto are and ba
Choose the Correct Answer
9. If and are vectors of magnitude then the
magnitude of is
(a) 2 (b) 3
(c) 2 (d) 1
10. If
then
(a) (b)
(c)
(d)
q , p
0 x 0 y
parallel are y and x
q p
q p
y x ) b a ( c ) a c ( b ) c b ( a
parallel are y and x or 0 y or 0 x
Choose the Correct Answer
11. If then the area of the quadrilateral PQRS is
(a) 53 (b) 103
(c) 53/2 (d) 3/2
12. If for non-coplanar vectors then
(a) (b)
(c) (d)
k j i 2 PR
c bacba
k 2 j 3 i QS
toparallel is ba
c , b , a
toparallel is c a
c toparallel is b
0 c b a
Choose the Correct Answer
13. The projection of on a unit vector equals thrice the area of the parallelogram OPRQ. Then POQ is
(a) (b)
(c) (d)
14. If
(a) 32 (b) 8
(c) 128 (d) 0
OP
isaccbba c , b , a then 64 , ,
OQ
3
1tan 1
10
3cos 1
10
3sin 1
3
1sin 1
Choose the Correct Answer
15. If the projection of on and projection of on are equal then the angle between is
(a) (b)
(c) (d)
16. If
(a) 4 (b) 16
(c) 32 (d) – 4
a
is c , b , a then 8 , , accbba
b
2
b a
b a and b a
3
3
24
Choose the Correct Answer
17. If a line makes 45°, 60° with positive direction of axes x and y then the angle it makes with the z axis is
(a) 30° (b) 90’
(c) 45° (d) 60°
18. The value of
(a) 0 (b) 1
(c) 2 (d) 4
, , ikkjji
Choose the Correct Answer
19. If are non-coplanar and
(a) 2 (b) 3
(c) 1 (d) 0
20. The shortest distance of the point (2, 10, 1) from the plane(a) 226 (b) 26
(c) 2 (d) 1/26
is 262 4 3 kjir
c , b , a then
a c , c b , b a accbba , ,
c , b , a
Choose the Correct Answer
21. The vector
(a)
(b)
(c)
(d)
and c , , lar toperpendicu dba
is d c b a
c and vectors the toparallel dba
and containing plane the
and and containing plane theof
onintersecti of line the toparallel
dc
ba
and containing plane the
and and containing plane theof
onintersecti of line thelar toperpendicu
dc
ba
Choose the Correct Answer
22. If are a right handed triad of mutually perpendicular vectors of magnitude a, b, c then the value of
(a) a2b2c2 (b) 0
(c) ½ abc (d) abc
23. is the equation of
(a) a straight line joining the points
(b) xoy plane
(c) yoz plane
(d) zox plane
c , , ba
is c , , ba
j i r ts
j i and
Choose the Correct Answer
24. If the magnitude of moment about the point of a force acting through the point is 8 then the value of a is
(a) 1 (b) 2
(c) 3 (d) 4
25. The work done by the force acting
on a particle, if the particle is displaced from
A(3, 3, 3), B(4, 4, 4) is
(a) 2 units (b) 3units
(c) 4units (d) 7units
kj
k j i F
kjai ji
Choose the Correct Answer
26. The equation of the line parallel to
and passing through the point (1, 3, 5) in vector form
is
(a)
(b)
(c)
(d)
3
52
5
3
1
3
zyx
5 3 3 5 kjitkjir
3 5 5 3 kjitkjir
5 3 2
3 5 kjitkjir
2
3 5 5 3 kjitkjir
Choose the Correct Answer
27. The equation of the plane passing through the point
(2, 1, -1) and the line of intersection of the planes
(a) x + 4y – z = 0
(b) x + 9y + 11z = 0
(c) 2x + y – z + 5 = 0
(d) 2x – y + z = 0
iskjrkjir 0 2 and 0 3
Choose the Correct Answer
27. The point of intersection of the line
and the plane
(a) (8, 6, 22)
(b) (– 8, – 6, – 22)
(c) (4, 3, 11)
(d) (– 4, – 3, – 1)
7 2 3 kjitkir
is 8 kjir
Choose the Correct Answer
28. If and then a
unit vector perpendicular to
(a)
(b)
(c)
(d)
3 2 kjia
3
kji
2 3 kjib
is and ba
3
kji
3
2 kji
3
kji
Choose the Correct Answer
29. The shortest distance between the lines
(a) (b)
(c) (d)
30. The following two lines are
(a) parallel (b) intersecting
(c) skew (d) perpendicular
is 5
5
4
4
3
2 and
4
3
3
2
2
1
zyxzyx
2
1
5
1
3
2 and
11
1
2
1
zyxzyx
3
2
3
26
1
62
1
Choose the Correct Answer
31. The shortest distance between the parallel lines
(a) 3
(b) 2
(c) 1
(d) 0
is 3
3
2
2
4
1 and
3
5
2
1
4
3
zyxzyx
Choose the Correct Answer
32. The point of intersection of the lines
(a) (0, 0, – 4)
(b) (1, 0, 0)
(c) (0, 2, 0)
(d) (1, 2, 0)
is 2
3
4
2
2
1 and
8
4
4
4
6
6
zyxzyx
Choose the Correct Answer
33. The point of intersection of the lines
(a) (2, 1, 1) (b) (1, 2, 1)
(c) (1, 1, 2) (d) (1, 1, 1)
2 3 2 kjitkjir
3 2 5 3 2 kjiskjir
Choose the Correct Answer
1. The value of if and
is
(a) 19 (b) 3
(c) – 19 (d) 14
2. The value of if and
is
(a) 2 (b) – 2
(c) 3 (d) 4
ba .
kjia 2
kjib 744
ba .
kja 2
kib 2
Choose the Correct Answer
1. The value of if and
is
(a) 7 (b) – 7
(c) 5 (d) 6
2. If and are
perpendicular then m is
(a) – 4 (b) 8
(c) 4 (d) 12
ba .
kja 2
kjib 232
kjim 2
kji 294