Calculate the area of the triangle determined by the two vectors →A=3^i+4^j and →B=−3^i+7^j
We know that the half of magnitude of the cross product of two vectors gives the area of the triangle.
→A×→B=∣∣ ∣ ∣∣^i^j^k340−370∣∣ ∣ ∣∣=^i(0−0)−^j(0−0)+^k(21+12)=33^k
Taking magnitude |→A×→B|=√332
So area of triangle =12|→A×→B|=332=16.5sq unit