If the projection of 2 i ^ + 4 j ^ - 2 k ^ on i ^ + 2 j ^ + α k ^ is zero. Then, the value of α will be

Given here: a → = 2 i ^ + 4 j ^ - 2 k ^ and b → = i ^ + 2 j ^ + α k ^ Now, a → · b → = 0 , as a → should be perpendicular to b → . ∴ 2 × 1 + 4 × 2 - 2 × α = 0 ∴ α = 5

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Physics - Vectors Question with Solution | TestHub

PhysicsVectorsMultiplication of vectorsEasy2 minPYQ_2022

PhysicsEasynumerical

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

Answer:

5.00

Solution:

Given here:
$\vec{a} = 2 \hat{i} + 4 \hat{j} - 2 \hat{k}$ and $\vec{b} = \hat{i} + 2 \hat{j} + α \hat{k}$
Now, $\vec{a} \cdot \vec{b} = 0$ , as $\vec{a}$ should be perpendicular to $\vec{b}$ .
$∴ 2 \times 1 + 4 \times 2 - 2 \times α = 0$
$∴ α = 5$

Stream:JEESubject:PhysicsTopic:VectorsSubtopic:Multiplication of vectors

⏱ 2mℹ️ Source: PYQ_2022

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