For non-zero vectors a , b , c ,|( a b ) c |=| a || b || c | holds if and only if
Mathematics · JEE Main · NTA Exams — Three Dimensional Geometry
For non-zero vectors \(\vec{a}, \vec{b}, \vec{c},|(\vec{a} \times \vec{b}) \cdot \vec{c}|=|\vec{a}||\vec{b}||\vec{c}|\)holds if and only if
- \(\vec{a} \cdot \vec{b}=0 \cdot \vec{b} \cdot \vec{c}=0\)
- \(\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0, \overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{~b}}=0\)
- \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{c}}=0 \cdot \overrightarrow{\mathrm{~b}} \cdot \overrightarrow{\mathrm{c}}=0\)
- \(\vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}=\vec{c} \cdot \vec{a}=0\)
Answer
(D) a b = b c = c a =0
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