Question

Calculate the area of the triangle for which two of its sides are given by the vectors A = 5i - 3j, B = 4i + 6j.

Answer 1

Given conditions ⇒

Vector A = 5i - 3j
Vector B = 4i + 6j

Let us find the Cross-products of these vectors, 
 (5i - 3j + 0k) × (4i + 6j + 0k) = (0i + 0k + 48k)

Using the Formula of the Area of the Triangle when two consecutive sides in vector forms is given.
∴ Area of the Δ = 1/2[A + B]
   = 1/2[0i + 0j + 48k]
   = 1/2($\sqrt{(0^{2} + (0)^{2} + (48)^{2} }$ )
   = 1/2($\sqrt{(48)^{2} }$)
   = 48/2
   = 21 unit²


Hence, the area of the triangle is 21 unit².


Hope it helps.