The area of the triangle formed by the two vectors →A = 3^i + 4^j and →B = −3^i + 7^j is
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 = 33.
So area of triangle = 12|→A × →B| = 332sq.unit