Let $\overrightarrow{\mathrm{a}}=3 \hat{i}+\hat{j}$ and $\overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}+\hat{k}$. Let $\overrightarrow{\mathrm{c}}$ be a vector satisfying $$\overrightarrow{\mathrm{a}} \times(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})=\overrightarrow{\mathrm{b}}+\lambda \overrightarrow{\mathrm{c}}$$. If $\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ are non-parallel, then the value of $\lambda$ is :
Solution
<p>$\overrightarrow a = 3\widehat i + \widehat j$ & $\overrightarrow b = \widehat i + 2\widehat j + \widehat k$</p>
<p>$$\overrightarrow a \times (\overrightarrow b \times \overrightarrow c ) = (\overrightarrow a \,.\,\overrightarrow c )\overrightarrow b - (\overrightarrow a \,.\,\overrightarrow b )\overrightarrow c = \overrightarrow b + \lambda \overrightarrow c $$</p>
<p>If $\overrightarrow b$ & $\overrightarrow c$ are non-parallel</p>
<p>then $\overrightarrow a \,.\,\overrightarrow c = 1$ & $\overrightarrow a \,.\,\overrightarrow b = - \lambda$</p>
<p>but $\overrightarrow a \,.\,\overrightarrow b = 5 \Rightarrow \lambda = - 5$</p>
About this question
Subject: Mathematics · Chapter: Vector Algebra · Topic: Types of Vectors
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