Mathematics in Physics

JEE Main level, numerical answer, medium

46 of 121

Question 46 of 121

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

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Answer: 5

Given here:
a⃗=2i^+4j^−2k^\vec{a}=2\hat{i}+4\hat{j}-2\hat{k} and b⃗=i^+2j^+αk^\vec{b}=\hat{i}+2\hat{j}+\alpha \hat{k}
Now, a⃗⋅b⃗=0\vec{a}\cdot \vec{b}=0, as a⃗\vec{a} should be perpendicular to b⃗\vec{b}.
∴2×1+4×2−2×α=0∴2\times 1+4\times 2-2\times \alpha =0
∴α=5∴\alpha =5

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