find the area of the parallelogram whose diagonals are along the vectors 2i and 3k - Maths - Vector Algebra

Question

find the area of the parallelogram whose diagonals are along the
vectors 2i and 3k

Lalit Mehra · Accepted Answer

The area of a parallelogram with diagonal $\vec{a} and \vec{b} is \frac{1}{2} | \vec{a} \times \vec{b} |$ $G i v e n, \vec{a} = 2 \hat{i} a n d \vec{b} = 3 \hat{j}$ $\vec{a} \times \vec{b} = 2 \hat{i} \times 3 \hat{k} = 6 \hat{i} \times \hat{k} = 6 (- \hat{j}) = - 6 \hat{j} | \vec{a} \times \vec{b} | = | - 6 \hat{j} | = 6 \times 1 = 6 [∵ | \hat{j} | = 1]$ âˆ´ Area of parallelogram $= \frac{1}{2} | \vec{a} \times \vec{b} | = \frac{1}{2} \times 6 = 3$