Find the area of a parallelogram whose adjacent sides are given by the vectors: and
Find the area of a parallelogram whose adjacent sides are given by the vectors:
$\vec{a} = \hat{\imath} - \hat{\jmath} + 3\hat{k}$ and $\vec{b} = 2\hat{\imath} - 7\hat{\jmath} + 4\hat{k}$
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
The area of the parallelogram is $|\vec{a} \times \vec{b}|$.
$\vec{a} \times \vec{b} = \begin{vmatrix} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 1 & -1 & 3 \\ 2 & -7 & 4 \end{vmatrix} = \hat{\imath}(-4 + 21) - \hat{\jmath}(4 - 6) + \hat{k}(-7 + 2) = 17\hat{\imath} + 2\hat{\jmath} - 5\hat{k}$.
Area $= \sqrt{17^2 + 2^2 + (-5)^2} = \sqrt{289 + 4 + 25} = \sqrt{318}\text{ sq units}$.
From ISC 2026 Mathematics Paper 1, question 15(iv).