Vector Algebra Question - CBSE

Question

If $\vec{a}, \vec{b}, \vec{c}$ are mutually perpendicular vectors of equal magnitudes, show that the vector $\vec{a} + \vec{b} + \vec{c}$ is equally inclined to $\vec{a}, \vec{b}$ and $\vec{c}$.

Accepted Answer

$|\vec{a}+\vec{b}+\vec{c}| = k\sqrt{3}$. [1.5 Marks]
$\cos\alpha = \cos\beta = \cos\gamma = \dfrac{1}{\sqrt{3}} \Rightarrow$ Equally inclined. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Evaluating magnitude of vector sum: 1.5 Marks
Proving all direction angles are equal to $\cos^{-1}(1/\sqrt{3})$: 1.5 Marks

Question:

Step-by-Step Solution

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