For non-zero vectors a , b , c ,|( a b ) c |=| a | b || c holds, if and only if

Mathematics · JEE Main · NTA Exams — Vector Algebra

For non-zero vectors \(\vec{a}, \vec{b}, \vec{c},|(\vec{a} \times \vec{b}) \cdot \vec{c}|=|\vec{a} \||\vec{b}|| \vec{c} \mid\) holds, if and only if

\(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{~b}}=0, \overrightarrow{\mathrm{~b}} \cdot \overrightarrow{\mathrm{c}}=0\)
\(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=0, \overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0\)
\(\vec{c} \cdot \vec{a}=0, \vec{a} \cdot \vec{b}=0\)
\(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=0\)

Answer

(D) a ~b = b c = c a =0

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