Vector Algebra
RS Aggarwal
CBSE
Grade 12
Question:
If $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = 3\hat{i} - \hat{j} + 2\hat{k}$, then $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$ are:
(a) Perpendicular
(b) Parallel
(c) Equal
(d) Opposite
Step-by-Step Solution
Key Concept: (a+b).(a-b) = |a|^2 - |b|^2 = 14 - 14 = 0.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: Perpendicular
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