Let $\vec a=3\hat i-\hat j+2\hat k$, $\vec b=\vec a imes(\hat i-2\hat k)$ and $\vec c=\vec b imes\hat k$. Then the projection of $\vec c-2\hat j$ on $\vec a$ is :

Question

Let $\vec a=3\hat i-\hat j+2\hat k$, $\vec b=\vec a	imes(\hat i-2\hat k)$ and $\vec c=\vec b	imes\hat k$. Then the projection of $\vec c-2\hat j$ on $\vec a$ is :

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $\vec b=(3,-1,2)	imes(1,0,-2)=(2,8,1)$ and $\vec c=\vec b	imes\hat k=(8,-2,0)$. So $\vec c-2\hat j=(8,-4,0)$. Projection on $\vec a$ $=\frac{(8,-4,0)\cdot(3,-1,2)}{\sqrt{14}}=\frac{28}{\sqrt{14}}=2\sqrt{14}$. Answer (1).

Q. Let $\vec a=3\hat i-\hat j+2\hat k$, $\vec b=\vec a\times(\hat i-2\hat k)$ and $\vec c=\vec b\times\hat k$. Then the projection of $\vec c-2\hat j$ on $\vec a$ is :

Explanation

Reviewed by Dr. Abubacker

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