Let $\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda0$ and the projection vector of $\vec{b}$ on $\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}$ is $\vec{c}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by vector $\vec{b}$ and $\vec{c}$ is (in square units)

Question

Let $\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0$ and the projection vector of $\vec{b}$ on $\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}$ is $\vec{c}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by vector $\vec{b}$ and $\vec{c}$ is (in square units)

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Let \(\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0\) and the projection vector of \(\vec{b}\) on \(\vec{a}=2 \hat{i}+…

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Let \(\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda&gt;0\) and the projection vector of \(\vec{b}\) on \(\vec{a}=2 \hat{i}+…

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Let \(\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0\) and the projection vector of \(\vec{b}\) on \(\vec{a}=2 \hat{i}+…