Let $\overrightarrow a = \widehat i + \widehat j + \widehat k,\overrightarrow b$ and $\overrightarrow c = \widehat j - \widehat k$ be three vectors such that $\overrightarrow a \times \overrightarrow b = \overrightarrow c$ and $\overrightarrow a \,.\,\overrightarrow b = 1$. If the length of projection vector of the vector $\overrightarrow b$ on the vector $\overrightarrow a \times \overrightarrow c$ is l, then the value of 3l2 is equal to _____________.
Answer (integer)
2
Solution
$\overrightarrow a \times \overrightarrow b = \overrightarrow c$<br><br>Take Dot with $\overrightarrow c$<br><br>$$\left( {\overrightarrow a \times \overrightarrow b } \right).\,\overrightarrow c = {\left| {\overrightarrow c } \right|^2} = 2$$<br><br>Projection of $\overrightarrow b$ or $\overrightarrow a \times \overrightarrow c = l$<br><br>$${{\left| {\overrightarrow b \,.\,(\overrightarrow a \times \overrightarrow c )} \right|} \over {|\overrightarrow a \times \overrightarrow c |}} = l$$<br><br>$\therefore$ $l = {2 \over {\sqrt 6 }} \Rightarrow {l^2} = {4 \over 6}$<br><br>$3{l^2} = 2$
About this question
Subject: Mathematics · Chapter: Vector Algebra · Topic: Types of Vectors
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