If the vectors $\hat{i}+2 \hat{\jmath}+x \hat{k}$ and $y t+6 \hat{k}+4 \hat{k}$ are collinear, then the values of $x$ and $y$ are respectively,

Question

Aicharya · Accepted Answer

Let $\bar{a} \& \bar{b}$ be given collinear vectors $\begin{array}{l} 	herefore \overline{\mathrm{a}}=\mathrm{m} \overline{\mathrm{b}} \ 	herefore \quad \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mathrm{x} \hat{\mathrm{k}}=\mathrm{m}(\mathrm{yi}+6 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}) \ 	herefore \quad \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mathrm{xk}=\mathrm{my} \hat{\mathrm{i}}+6 \mathrm{~m} \hat{\mathrm{j}}+4 \mathrm{mk} \ 	herefore \quad 1=\mathrm{my}, 2=6 \mathrm{~m}, \mathrm{x}=4 \mathrm{~m} \Rightarrow \mathrm{m}=\frac{1}{3}, \mathrm{y}=3, \mathrm{x}=\frac{4}{3} \end{array}$

If the vectors $\hat{i}+2 \hat{\jmath}+x \hat{k}$ and $y t+6 \hat{k}+4 \hat{k}$ are collinear, then the…

Solution