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Question

Question: <img src="https://cdn.pureessence.tech/canvas_306.png?top_left_x=0&top_left_y=717&width=300&height=4...

A

3r23 r ^ { 2 }

B

r2r ^ { 2 }

C

0

D

None of these

Answer

r2r ^ { 2 }

Explanation

Solution

Let r=xi+yj+zk\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }

⇒(r⋅i)2+(r⋅j)2+(r⋅k)2=x2+y2+z2=r2\Rightarrow ( \mathbf { r } \cdot \mathbf { i } ) ^ { 2 } + ( \mathbf { r } \cdot \mathbf { j } ) ^ { 2 } + ( \mathbf { r } \cdot \mathbf { k } ) ^ { 2 } = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = r ^ { 2 }