Vector Algebra One Mark Questions

PREPARED BY:R.RAJENDRAN. M.A., M. SC., M. ED.,K.C.SANKARALINGA NADAR HR. SEC. SCHOOL,CHENNAI-21

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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