Question

For the following two vectors, A = -5 i + 7 j + 4 k and B = 8 i + 3 j – 7 k ;
a. What is the scalar product, (give answers in both component form and magnitude/direction form)?
b. What is the angle between them in the same plane?
c. What is the vector product, (give answers in both component form and magnitude/direction form)?

Answer 1

here,

A = - 5 i + 7 j + 4 k

B = 8 i + 3 j - 7 k

a)

the scaler product , A . B = (- 5 i + 7 j + 4 k) . (8 i + 3 j - 7 k)

A.B = ( - 40 + 21 - 28) = -47 units

b)

the angle between them in the same plane , theta = arccos(A.B /(|A||B|) )

theta = arccos( 47 /9.49 * 11)

theta = 63.2 degree

c)

the vector product,A X B = (- 5 i + 7 j + 4 k) X (8 i + 3 j - 7 k)

A X B = ( - 15 k - 35 j - 56 k - 49 i + 32 j - 12 i) = ( - 51 i -3 j - 24 k)