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Vector Algebra
Oswaal
CBSE
Grade 12

Question:

Area of parallelogram with adjacent sides $\vec{a} = \hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} - 7\hat{j} + \hat{k}$ is:
(a) $15\sqrt{2}$ sq units
(b) $15$ sq units
(c) $30$ sq units
(d) $5\sqrt{2}$ sq units

Step-by-Step Solution

Key Concept: |a x b| = |20i + 5j - 5k| = \sqrt{400 + 25 + 25} = \sqrt{450} = 15\sqrt{2}.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: $15\sqrt{2}$ sq units
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