Mathematics › Vectors › Product of 2 vectors
If $\mathbf{a}$ makes an acute angle with $\mathbf{b}, \mathbf{r} \cdot \mathbf{a}=0$ and $\mathbf{r} \times…
If $\mathbf{a}$ makes an acute angle with $\mathbf{b}, \mathbf{r} \cdot \mathbf{a}=0$ and $\mathbf{r} \times \mathbf{b}=\mathbf{c} \times \mathbf{b}$, then $\mathbf{r}=$
$\mathbf{a} \times \mathbf{c}-\mathbf{b}$ $c \times a$ $c-\left(\frac{c \cdot a}{b \cdot a}\right) b$ $c+\left(\frac{c \cdot a}{b \cdot a}\right) b$ Solution
Given,
and
$
\begin{aligned}
\mathbf{r} \cdot \mathbf{a} & =0 \\
\mathbf{r} \times \mathbf{b} & =\mathbf{c} \times \mathbf{b}
\end{aligned}
$
So,
$
\mathbf{r} \times \mathbf{b}=\mathbf{c} \times \mathbf{b}
$
$
\begin{aligned}
& \mathbf{r}(\mathbf{a} \cdot \mathbf{b})-\mathbf{b}(\mathbf{a} \cdot \mathbf{r})=\mathbf{c}(\mathbf{a} \cdot \mathbf{b})-\mathbf{b}(\mathbf{a} \cdot \mathbf{c}) \\
& \Rightarrow \quad \mathbf{r}(\mathbf{a} \cdot \mathbf{b})=\mathbf{c}(\mathbf{a} \cdot \mathbf{b})-\mathbf{b}(\mathbf{a} \cdot \mathbf{c}) \\
& \Rightarrow \quad \mathbf{r}=\mathbf{c}-\mathbf{b}\left(\frac{\mathbf{c} \cdot \mathbf{a}}{\mathbf{a} \cdot \mathbf{b}}\right) \\
&
\end{aligned}
$
Asked in: AP EAMCET 2019 (21 Apr Shift 1)
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