If the projection of the vector $\widehat i + 2\widehat j + \widehat k$ on the sum of the two vectors $2\widehat i + 4\widehat j - 5\widehat k$ and $- \lambda \widehat i + 2\widehat j + 3\widehat k$ is 1, then $\lambda$ is equal to __________.
Answer (integer)
5
Solution
$\overrightarrow a = \widehat i + 2\widehat j + \widehat k$<br><br>$\overrightarrow b = (2 - \lambda )\widehat i + 6\widehat j - 2\widehat k$<br><br>$${{\overrightarrow a \,.\,\overrightarrow b } \over {|\overrightarrow b |}} = 1,\overrightarrow a \,.\,\overrightarrow b = 12 - \lambda $$<br><br>$$\left( {\overrightarrow a \,.\,\overrightarrow b } \right) = |\overrightarrow b {|^2}$$<br><br>$\lambda$<sup>2</sup> $-$ 24$\lambda$ + 144 = $\lambda$<sup>2</sup> $-$ 4$\lambda$ + 4 + 40<br><br>20$\lambda$ = 100 $\Rightarrow$ $\lambda$ = 5
About this question
Subject: Mathematics · Chapter: Vector Algebra · Topic: Types of Vectors
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