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Vector Algebra

Question

Find ' $λ$ ' when the projection of $\vec{a} = λ \hat{i} + \hat{j} + 4 \hat{k} on \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k}$ is 4 units.

Solution

$Projection of \vec{a} on \vec{b} = \frac{\vec{a} . \vec{b}}{|\vec{b}|} = 4 (given) \Rightarrow \frac{(λ \hat{i} + \hat{j} + 4 \hat{k}) . (2 \hat{i} + 6 \hat{j} + 3 \hat{k})}{\sqrt{2^{2} + 6^{2} + 3^{2}}} = 4 \Rightarrow \frac{2 λ + 6 + 12}{7} = 4 \Rightarrow λ = 5 .$

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Vector Algebra

Find ' $λ$ ' when the projection of $\vec{a} = λ \hat{i} + \hat{j} + 4 \hat{k} on \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k}$ is 4 units.

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For Daily Free Study Material Join wiredfaculty

Vector Algebra

Find ' λ ' when the projection of a→ = λ i^ + j^ + 4 k^ on b→ = 2 i^ + 6 j^ + 3 k^ is 4 units.

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find ' $λ$ ' when the projection of $\vec{a} = λ \hat{i} + \hat{j} + 4 \hat{k} on \vec{b} = 2 \hat{i} + 6 \hat{j} + 3 \hat{k}$ is 4 units.