A vector ( d ) is equally inclined to three vectors a = i - j + k , b =2 i + j and c =3 j…
Mathematics · JEE Advanced · NTA Exams — Three Dimensional Geometry
A vector \((\overrightarrow{\mathrm{d}})\) is equally inclined to three vectors \(\vec{a}=\hat{i}-\hat{j}+\hat{k},\) \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{c}}=3 \hat{\mathrm{j}}-2 \hat{\mathrm{k}} .\) Let \(\overrightarrow{\mathrm{x}}, \overrightarrow{\mathrm{y}}, \overrightarrow{\mathrm{z}}\) be three vector in the plane of \(\vec{a}, \vec{b} ; \vec{b}, \vec{c} ; \vec{c}, \vec{a}\) respectively then
- \(\overrightarrow{\mathrm{x}} \cdot \overrightarrow{\mathrm{~d}}=4\)
- \(\vec{y} \cdot \vec{d}=3\)
- \(\vec{z} \cdot \vec{d}=0\)
- \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{~d}}=0\) where \(\overrightarrow{\mathrm{r}}=\lambda \overrightarrow{\mathrm{x}}+\mu \overrightarrow{\mathrm{y}}+\delta \overrightarrow{\mathrm{z}}\)
Answer
(C) z d =0, (D) r ~d =0 where r = x + y + z
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