Question

If angle between 2 vector p vector and q vector is 60° and magnitude of resultant of this vector is √7×q, then find the value of p/q.

Answer 1

Answer with explanation:

it is given that, angle between 2 vector p vector and q vector is 60° and magnitude of resultant of this vector is √7×q.

→p+q-√7 q=0→→[Sum of vectors, represented as a sides in a triangle is equal to 0.]

→p+q=√7 q

Squaring both sides

→p²+q²+2 p q cos 60°=(√7 q)²

→p²+q²+2 p q×$\frac{1}{2}$=7 q²

→p²+q²+ p q-7 q²=0

→p²-6 q²+ p q=0

→p²+p q=6 q²

→p(p+q)=6 q²⇒⇒using distributive property

→p × √7 q=6 q²

Cancelling vector 'q' from both sides

→p × √7=6 q

$\frac{p}{q}=\frac{6}{\sqrt{7}}$