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Solve the following.
Find if the scalar projection of on is units.
Find $\lambda$ if the scalar projection of $\vec{a} = \lambda\hat{\imath} + \hat{\jmath} + 4\hat{k}$ on $\vec{b} = 2\hat{\imath} + 6\hat{\jmath} + 3\hat{k}$ is $4$ units.
Answer
Answer
AIScalar projection of $\vec a$ on $\vec b = \frac{\vec a\cdot\vec b}{|\vec b|}$.
$\vec a\cdot\vec b = 2\lambda + 6 + 12 = 2\lambda + 18$, $|\vec b| = \sqrt{4+36+9} = 7$.
$\frac{2\lambda+18}{7} = 4 \Rightarrow 2\lambda = 10$
Hence $\lambda = 5$.
Final answer: 5
From ISC 2018 Mathematics Paper 1, question 15(a).
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