Given vectors A= - 4.2i + 7.9j and B= 9.6i + 6.7j, determine the vector C?

Question

Given vectors A= -4.2i + 7.9j and B= 9.6i + 6.7j , determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

I can't seem to figure out how to set this up, I would appreciate any help that I can get! Thanks in advance.

Answer 1

Because C is in xy-plane it must have the form:

C = x·i + y·j

C is perpendicular to B. Thta means the the dor product of B and C equals zero

B·C = 0

=>

(i)  9.6·x + 6.7·y = 0

The dot product of A and C equals 20

A·C = 20

=>

(ii)  -4.2·x + 7.9·y = 20

From (i) follows that

y = -(9.6/6.7)·x

Substitute to (ii)

-4.2·x - 7.9·(9.6/6.7) ·x = 20

=>

x = -20·6.7 / (4.2·6.7 + 7.9·9.6)

= - 134 / 103.98 ≈ -1.2887

=>

y = -(9.6/6.7) · (-134/103.98)

= 192 / 103.98 ≈ 1.8465