Question

Two forces are such that the sum of thier is 18 N magnitude of the resultant is 12 N and thier resultant is perpendicular to the smaller force then the magnitude of the product vector A ( Vector B× vector A) is-​

Answer 1

let the smaller force be B, the larger force be A, resultant being C.

Given : |A| + |B| = 18, |C| = 12

A,B,C simply form a right angle triangle with base B vector ,hypotenus being A

So, you have one equation with you : A + B = 18

${a}^{2} = {b}^{2} + {c}^{2}$

${a}^{2} - {c}^{2} = {b}^{2}$

$(a + b)(a - b) = 144$

$(a - b)18 = 144$

$a - b = \frac{144}{18} = 18$

so simply solving both equations

= A - B = 8 and

= A + B = 18

add both

2a = 26

A = 13

B = 5