Question

If $( ( \vec { a } \times \vec { b } ) \times ( \vec { c } \times \vec { d } ) )$. (×) = 0, then which of the following is always true-

• A. , , $\overrightarrow { \mathrm { c } }$, are necessarily coplanar
• B. Either or must lie in the plane of and$\overrightarrow { \mathrm { c } }$
• C. Either or $\overrightarrow { \mathrm { c } }$ must lie in plane of and
• D. Either or must lie in plane of $\overrightarrow { \mathrm { c } }$ and

Answer 1

Answer: (C)

Either or $\overrightarrow { \mathrm { c } }$ must lie in plane of and

Answer 2

$( ( \vec { a } \times \vec { b } ) \times ( \vec { c } \times \vec { d } ) )$. $( \vec { a } \times \vec { d } )$ = 0

Ž . $( \vec { a } \times \vec { d } )$= 0

Ž [$\overrightarrow { \mathrm { c } }$] [ $\overrightarrow { \mathrm { b } }$ ] = 0

Ž either $\overrightarrow { \mathrm { c } }$ or $\overrightarrow { \mathrm { b } }$ must lie in the plane of and .