If $\overrightarrow{\mathrm{A}}=a_{1} \hat{\imath}+a_{2} \hat{\jmath}$ and…

If $\overrightarrow{\mathrm{A}}=a_{1} \hat{\imath}+a_{2} \hat{\jmath}$ and $\overrightarrow{\mathrm{B}}=b_{1} \hat{\imath}+b_{2} \hat{\jmath}$ are perpendicular to each other then
  1. $\frac{\mathrm{b}_{2}}{\mathrm{a}_{1}}=-\frac{\mathrm{a}_{2}}{\mathrm{~b}_{1}}$
  2. $\frac{\mathrm{a}_{1}}{\mathrm{~b}_{2}}=+\frac{\mathrm{a}_{2}}{\mathrm{~b}_{1}}$
  3. $\frac{\mathrm{b}_{2}}{\mathrm{a}_{1}}=+\frac{\mathrm{a}_{2}}{\mathrm{~b}_{1}}$
  4. $\frac{a_{1}}{b_{2}}=-\frac{\mathrm{a}_{2}}{\mathrm{~b}_{1}}$

Solution

When two vectors are perpendicular, the cross product of the two vectors is zero A. $B=0$ $a_1 b_1+a_2 b_{\overline{2}} 0$ $-a_1 b_1=a_2 b_2$ $\frac{\mathrm{a}_1}{\mathrm{~b}_2}=-\frac{\mathrm{a}_2}{\mathrm{~b}_1}$

Asked in: MHT CET 2020 (15 Oct Shift 2)

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