Question

Show that the area of the triangle contained between the vectors vector(a and b) is one half rate of the magnitude of vector(a x b)

Answer 1

Let vector OP represents vector a and vector OQ represents vector b and ∠POQ = θ = In || gm OPRQ Draw QN ⊥ OP

In ΔOQN,

Sinθ = QN/OQ = QN/b

Or, QN = b sinθ

Now, by definition,

|vector(a x b)| = ab sinθ

(OP)(QN) = {2(OP)(QN)}/{2}

= 2 x ar (ΔOPQ)

Area of ΔOPQ = 1/2 |vector(a x b)| Proved