Let $\vec c$ be the projection vector of $\vec b=\lambda\hat i+4\hat k$, $\lambda0$, on the vector $\vec a=\hat i+2\hat j+2\hat k$. If $|\vec a+\vec c|=7$, then the area of the parallelogram formed by the vectors $\vec b$ and $\vec c$ is _______

Question

Let $\vec c$ be the projection vector of $\vec b=\lambda\hat i+4\hat k$, $\lambda>0$, on the vector $\vec a=\hat i+2\hat j+2\hat k$. If $|\vec a+\vec c|=7$, then the area of the parallelogram formed by the vectors $\vec b$ and $\vec c$ is _______

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $\vec c=\frac{\lambda+8}9\vec a$, so $\vec a+\vec c=\frac{\lambda+17}9\vec a$ and $|\vec a+\vec c|=\frac{\lambda+17}3=7\Rightarrow\lambda=4$. Then $\vec b=(4,0,4)$, $\vec c=\frac43(1,2,2)$ and $|\vec b	imes\vec c|=\frac{16}3\cdot3=16$. Answer: 16.

Q. Let $\vec c$ be the projection vector of $\vec b=\lambda\hat i+4\hat k$, $\lambda>0$, on the vector $\vec a=\hat i+2\hat j+2\hat k$. If $|\vec a+\vec c|=7$, then the area of the parallelogram formed by the vectors $\vec b$ and $\vec c$ is _______

Explanation

Reviewed by Dr. Abubacker

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