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Question

If the vectors $$\overrightarrow { k } $$ and $$\overrightarrow { A } $$ are parallel to each other, then what is $$k\overrightarrow { k } \times \overrightarrow { A } $$ equal to?


A
k2A
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B
0
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C
k2A
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D
A
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Solution

The correct option is A $${ k }^{ 2 }\overrightarrow { A } $$
Here, the left $$k$$ in the equation is a scalar

Now, Vector Product $$k\vec{k}$$ x$$\vec{A}=k.\vec{k}.\vec{A}.sin\theta=|k^2|\vec{A}.sin\theta$$

and since, these lines are Parallel $$\theta=0\Rightarrow sin\theta=1$$
$$|k^2|\vec{A}.sin\theta=|k^2|\vec{A}=k^2\vec{A}$$

Therefore, Answer is $$A$$

Mathematics

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