Let A(2,3,5) and C(-3,4,-2) be opposite vertices of a parallelogram A B C D.

Question

Let $A(2,3,5)$ and $C(-3,4,-2)$ be opposite vertices of a parallelogram $A B C D$. If the diagonal $$\overrightarrow{\mathrm{BD}}=\hat{i}+2 \hat{j}+3 \hat{k}$$, then the area of the parallelogram is equal to :

Accepted Answer

$$\begin{aligned}
& \text { Area }=|\overrightarrow{\mathrm{AC}} \times \overrightarrow{\mathrm{BD}}| \
& =\left|\[\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \ 5 & -1 & 7 \ 1 & 2 & 3 \end{array}\end{aligned}$$\right| \
\& =\frac{1}{2}|-17 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+11 \hat{\mathrm{k}}|=\frac{1}{2} \sqrt{474}
\]

Solutions · 1