Vectors crash course

DPP

1. The angle made by the vector with x - axis is

A

B

D

C

450

22.50

300

900

2. If a vector making angles ∝, β, and γ respectively with the x, y and z axes

respectively.

Then sin2 α + sin2 β + sin2 γ =

A

B

D

C

1

2

3

0

3. One of rectangular components of a velocity of 30 ms-1 is 20 ms-1. Find the other component.

A

B

D

C

4. To go from town A to town B a plane must fly about 1780 km at an angle of 600 West of north. How far north of A is B?

A

B

D

C

1452 km

1254 km

11 km

890 km

A

B

D

C

5. If , its components in yz plane and zx plane are respectively

6. A car is moving 20m due east, turns towards north moves 40m. Then turns 450 east of north & moves 20 . The net displacement of car is (East is taken positive x -axis, North as positive y - axis)

A

B

D

C

7. If and, then R2 + S2 is equal to

A

B

D

C

2(P2 - Q2)

2(P2 + Q2)

4 PQ

P2 + Q2

8. Two vectors have equal magnitudes of 10 units. These vectors are making angles 600 and 1350 with the x axis respectively. Their sum is 10k. Find the x and y components of the resultant.

A

B

D

C

10, 0

10, 10

5, 10

0, 10

9. If A = 4i - 4j units, B = 2i + 6j units and C = 10i + 6j units, determine a and b

when aA + bB + C =0

A

B

D

C

a = -1.5, b = -2

a = 0.9, b = 3.93

a = 0.6, b = -3

a = 0.4, b = 0.8

10. At what angle two vectors of magnitudes A + B and A - B act, so that their

resultant is

A

B

D

C

45o

60o

90o

30o

11. Two equal forces (P each) act at a point inclined to each other at an angle of 1200. The magnitude of their resultant is

A

B

D

C

2P

P

12. There are two force vectors, one of 5 N and other of 12 N. At what angle the two vectors be added to get resultant vector of 17 N, 7 N and 13 N respectively.

A

B

D

C

00, 900 and 1800

00, 900 and 900

1800, 00 and 900

00, 1800 and 900

13. If then which of the following statements is wrong

A

B

D

C

14. Two vectors are at right angles to each other, when

A

B

D

C

15. The cross product of the vectors

A

B

D

C

16. If = 2i - j - 3k and = 4i + 3j +2k, the unit vector perpendicular to both

and is

A

B

D

C

17. If and , component of along is

A

B

D

C

18. If and then vector perpendicular to

both and has magnitude K times that of . Then K =

A

B

D

C

3

1

9

7

19. If a, b are the unit of vectors, If the value of is

A

B

D

C

0

a b

a / b

20. If θ is the angle between unit vectors then is equal to

A

B

D

C

21. If then the value of

A

B

D

C

A + B

22. The value of

A

B

D

C

A2 - B2

0

23. If the value of then

A

B

D

C

25 N

100 N

169 N

5 N

24. Three vectors satisfy the relation . The

vector is parallel to

A

B

D

C

25. What is the angle between

A

B

D

C

π

0

26. The area of the parallelogram represented by the vectors

A

B

D

C

7.5 units

10 units

5 units

14 units

27. The vector are perpendicular to each

other. The positive value of a is

A

B

D

C

4

9

13

3

28. The angle between two vectors

A

B

D

C

90o

180o

None of the above

0o

29. If for two vectors the vectors

A

B

D

C

Are parallel to each other

Act at an angle of 60o

Act at an angle of 30o

Are perpendicular to each other

30. The angle between the vectors . The value of the triple product

A

B

D

C

Zero

A2 B sin θ

A2 B cos θ

A2B

Vectors crash course

SOLUTIONS

1. The angle made by the vector with x - axis is

A

B

D

C

450

22.50

300

900

Solution :

2. If a vector making angles ∝, β, and γ respectively with the x, y and z axes

respectively.

Then sin2 α + sin2 β + sin2 γ =

A

B

D

C

1

2

3

0

Solution :

3. One of rectangular components of a velocity of 30 ms-1 is 20 ms-1. Find the other component.

A

B

D

C

Solution :

4. To go from town A to town B a plane must fly about 1780 km at an angle of 600 West of north. How far north of A is B?

A

B

D

C

1452 km

1254 km

11 km

890 km

Solution :

A

B

D

C

5. If , its components in yz plane and zx plane are respectively

Solution :

6. A car is moving 20m due east, turns towards north moves 40m. Then turns 450 east of north & moves 20 . The net displacement of car is (East is taken positive x -axis, North as positive y - axis)

A

B

D

C

Solution :

7. If and, then R2 + S2 is equal to

A

B

D

C

2(P2 - Q2)

2(P2 + Q2)

4 PQ

P2 + Q2

Solution :

8. Two vectors have equal magnitudes of 10 units. These vectors are making angles 600 and 1350 with the x axis respectively. Their sum is 10k. Find the x and y components of the resultant.

A

B

D

C

10, 0

10, 10

5, 10

0, 10

Solution :

9. If A = 4i - 4j units, B = 2i + 6j units and C = 10i + 6j units, determine a and b

when aA + bB + C =0

A

B

D

C

a = -1.5, b = -2

a = 0.9, b = 3.93

a = 0.6, b = -3

a = 0.4, b = 0.8

Solution :

10. At what angle two vectors of magnitudes A + B and A - B act, so that their

resultant is

A

B

D

C

45o

60o

90o

30o

Solution :

11. Two equal forces (P each) act at a point inclined to each other at an angle of 1200. The magnitude of their resultant is

A

B

D

C

2P

P

Solution :

12. There are two force vectors, one of 5 N and other of 12 N. At what angle the two vectors be added to get resultant vector of 17 N, 7 N and 13 N respectively.

A

B

D

C

00, 900 and 1800

00, 900 and 900

1800, 00 and 900

00, 1800 and 900

Solution :

13. If then which of the following statements is wrong

A

B

D

C

Solution :

AXB and C are equal vectors, so they cannot be perpendicular to each other

14. Two vectors are at right angles to each other, when

A

B

D

C

Solution :

15. The cross product of the vectors

A

B

D

C

Solution :

16. If = 2i - j - 3k and = 4i + 3j +2k, the unit vector perpendicular to both

and is

A

B

D

C

Solution :

17. If and , component of along is

A

B

D

C

Solution :

18. If and then vector perpendicular to

both and has magnitude K times that of . Then K =

A

B

D

C

3

1

9

7

Solution :

19. If a, b are the unit of vectors, If the value of is

A

B

D

C

0

a b

a / b

Solution :

20. If θ is the angle between unit vectors then is equal to

A

B

D

C

Solution :

21. If then the value of

A

B

D

C

A + B

Solution :

22. The value of

A

B

D

C

A2 - B2

0

Solution :

23. If the value of then

A

B

D

C

25 N

100 N

169 N

5 N

Solution :

24. Three vectors satisfy the relation . The

vector is parallel to

A

B

D

C

Solution :

25. What is the angle between

A

B

D

C

π

0

Solution :

26. The area of the parallelogram represented by the vectors

A

B

D

C

7.5 units

10 units

5 units

14 units

Solution : Area of a parallelogram formed by the two vectors is given by

27. The vector are perpendicular to each

other. The positive value of a is

A

B

D

C

4

9

13

3

Solution :

28. The angle between two vectors

A

B

D

C

90o

180o

None of the above

0o

Solution :

29. If for two vectors the vectors

A

B

D

C

Are parallel to each other

Act at an angle of 60o

Act at an angle of 30o

Are perpendicular to each other

Solution :

30. The angle between the vectors . The value of the triple product

A

B

D

C

Zero

A2 B sin θ

A2 B cos θ

A2B

Solution :

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