Question

vector A=5i^+7j^-5k^,vectorB=4i^-7j^+6k^.check these two vectors are (a) parallel (b) perpendicular​

Answer 1

Just as a note, you mean the value of “a”, not the value of “A.” A is given as a fixed vector.

Vectors that are perpendicular to one another have zero inner product:

A . B = 5*2 + 7*2 + 3*a = 0

Note that the last operator is + because both vectors have negative k components; the product of two negatives is a positive.

This is easy to solve:

10 + 14 + 3a = 0

3a = -24

a = -8.