Let $$\overrightarrow a = - \widehat i - \widehat j + \widehat k,\overrightarrow a \,.\,\overrightarrow b = 1$$ and $\overrightarrow a \times \overrightarrow b = \widehat i - \widehat j$. Then $\overrightarrow a - 6\overrightarrow b$ is equal to :
Solution
$$
\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})
$$<br/><br/>
Taking cross product with $\vec{a}$<br/><br/>
$$
\begin{aligned}
& \Rightarrow \vec{a} \times(\vec{a} \times \vec{b})=\vec{a} \times(\hat{i}-\hat{j}) \\\\
& \Rightarrow (\vec{a} \cdot \vec{b}) \vec{a}-(\vec{a} \cdot \vec{a}) \vec{b}=\hat{i}+\hat{j}+2 \hat{k} \\\\
& \Rightarrow \vec{a}-3 \vec{b}=\hat{i}+\hat{j}+2 \hat{k} \\\\
& \Rightarrow 2 \vec{a}-6 \vec{b}=2 \hat{i}+2 \hat{j}+4 \hat{k} \\\\
& \Rightarrow \vec{a}-6 \vec{b}=3 \hat{i}+3 \hat{j}+3 \hat{k}
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Vector Algebra · Topic: Types of Vectors
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