Vector Algebra Question - CBSE

Question

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 5$ and $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, find the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$. Also find the angle between $\vec{a}$ and $\vec{b}$.

Accepted Answer

$|\vec{a}+\vec{b}+\vec{c}|^2 = 0 \Rightarrow 50 + 2S = 0 \Rightarrow S = -25$. [2.5 Marks]
$\vec{a}+\vec{b} = -\vec{c} \Rightarrow 9 + 16 + 24\cos heta = 25 \Rightarrow 24\cos heta = 0 \Rightarrow heta = \pi/2$. [2.5 Marks]

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🎯 Official CBSE Marking Scheme:
Evaluating pairwise dot product sum $S = -25$: 2.5 Marks
Evaluating angle between $\vec{a}$ and $\vec{b}$ $ heta = \pi/2$: 2.5 Marks

Question:

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