Vectors (from Activity)

Question 1

Find the magnitude of vector V = 2i- 5j.

Answer 1

√29 or approximately 5.39

Question 2

Find the direction cosines and direction angles of the vector A = 2i- 3j + 4k.

Answer 2

i = 0.37, j = -0.56, k = 0.74, θi = 68.20°, θj = 123.85°, θk = 42.03°

Question 3

Find the dot product of the vectors A= 3i + 4j- k and B = i + 2j + 3k.

Answer 3

8

Question 4

Find the angle between the vectors A= 3i + 4j- k and B = i + 2j + 3k.

Answer 4

65.21°

Question 5

Find the vector product( cross product ) of the vectors A= 3i + 4j- k and B = i + 2j + 3k.

Answer 5

14i - 10j + 2k

Question 6

Find the sum of the 2 vectors A = 3i- 5k and B = 2i + 4j- k.

Answer 6

5i + 4j - 6k

Question 7

A force vector F = 2i + 3j is applied to a particle and its moves the particle from ( 1, 2 ) to ( 5, 8 ). Find the work done by the force. Force in N and distance in m.

Answer 7

26 J

Question 8

Find the area of a parallelogram with vertices at A( 1, 2, 3 ), B( 1, 3, 6 ), C( 3, 8, 6 ), and D( 3, 7, 3 ).

Answer 8

16.28 m²

Question 9

Find the volume of a parallelepiped determined by the vectors a=  6, 3,- 1 , b = 0, 1, 2 , and c =  4,- 2, 5 

Answer 9

82 m³

Question 10

The vectors A = 2i- yj + 5k is parallel to vector B = 4i + 6j + 10k. Find y.

Answer 10

-3

Question 11

Angle between vectors formula

Answer 11

cos⁡θ= (A * B)/|A||B|