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  4. If the projection of 2 hati+4 hatj-2 hatk on hati+2 hatj+α hatk is zero. Then, the value of α will be

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Q. If the projection of $2 \hat{i}+4 \hat{j}-2 \hat{k}$ on $\hat{i}+2 \hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be

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Solution:

$ \overrightarrow{ a } \cdot \overrightarrow{ b }=0 $
$ \therefore \overrightarrow{ a } \cdot \overrightarrow{ b }=0$
$ \therefore 2 \times 1+4 \times 2-2 \times \alpha=0 $
$ \therefore \alpha=5$