Vectors

Question 1

Two forces PQ and PR of magnitude 5.0 kilograms and 8.0 kilograms respectively, act at a point P. The direction of PQ is N 20° E, and the direction of PR is N 65° E. Approximate the magnitude and direction of the resultant PS.

Answer 1

12.10 kg, N 48° E

Question 2

Find 2A if A = 2i - 4j - 5k.

Answer 2

4i - 8j -10k

Question 3

The magnitude and direction of a constant force are given by a = 2i + 5j. Find the work done if the point of application of the force moves from the origin to the point P( 4, 1 ).

Answer 3

W = 13 ft lb

Question 4

Find the angle between the vectors 3i + 2j + 5k and -4i + j + 6k.

Answer 4

θ = 63.53°

Question 5

Find the value of b if the vectors A = 2i + bj + 2k and B = 3i + 2j + k are perpendicular.

Answer 5

b = -4

Question 6

Find the area of a parallelogram with two sides identified by vectors from the origin to the points ( 3, 4 ) and ( 8, 0 ).

Answer 6

32

Question 7

Find the value of c if the vectors A = 2i - j + ck and B = 4i - 2j + 6k are parallel.

Answer 7

3