If z _ 1 =a i +b j & z _ 2 =c i +d j are two vectors in i j system where | z _ 1 |= | z _…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
If \(\vec{z}_{1}=a \hat{i}+b \hat{j}\) & \(\vec{z}_{2}=c \hat{i}+d \hat{j}\) are two vectors in \(\hat{i} \& \hat{j}\) system where \(\left|\overrightarrow{\mathrm{z}}_{1}\right|=\left|\overrightarrow{\mathrm{z}}_{2}\right|=\mathbf{r}\) & \(\vec{z}_{1} \cdot \vec{z}_{2}=0\) then \(\overrightarrow{\mathrm{w}}_{1}=\mathrm{a} \hat{\mathrm{i}}+\mathrm{c} \hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{w}}_{2}=\mathrm{b} \hat{\mathrm{i}}+\mathrm{d} \hat{\mathrm{j}}\) satisfy
- \(\left|\overrightarrow{\mathrm{w}}_{1}\right|=\mathrm{r}\)
- \(\left|\overrightarrow{\mathrm{w}}_{2}\right|=\mathrm{r}\)
- \(\overrightarrow{\mathrm{w}}_{1} \cdot \overrightarrow{\mathrm{w}}_{2}=0\)
- none of these
Answer
(A) | w _ 1 |= r, (B) | w _ 2 |= r, (C) w _ 1 w _ 2 =0
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