QJEEM11Ma7f68: JEE Main 2011 Physics - Class 11 JEEM11Ma7f68 Solution: The vectors and are not perpendicular and and are two vectors…

Question

Verified Solution • 2025–26 Session moderate

The vectors

\overrightarrow a

and

\overrightarrow b

are not perpendicular and

\overrightarrow c

and

\overrightarrow d

are two vectors satisfying

\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d

and

\overrightarrow a .\overrightarrow d = 0\,\,.

Then the vector

\overrightarrow d

is equal to :

A $\overrightarrow c + \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b$
B $\overrightarrow b + \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c$
C $\overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b$
D $\overrightarrow b - \left( {{{\overrightarrow b .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow c$

Accepted Answer

\overrightarrow a .\overrightarrow b \ne 0,\overrightarrow a .\overrightarrow d = 0

Now,

\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d

\Rightarrow \overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = \overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow d } \right)

\Rightarrow \left( {\overrightarrow a .\overrightarrow c } \right)\overrightarrow b - \left( {\overrightarrow a .\overrightarrow b } \right)\overrightarrow c = \left( {\overrightarrow a .\overrightarrow d } \right)\overrightarrow b - \left( {\overrightarrow a .\overrightarrow b } \right)\overrightarrow d

\Rightarrow \left( {\overrightarrow a .\overrightarrow b } \right)\overrightarrow d = - \left( {\overrightarrow a .\overrightarrow c } \right)\overrightarrow b + \left( {\overrightarrow a .\overrightarrow b } \right)\overrightarrow c

\overrightarrow d = \overrightarrow c - \left( {{{\overrightarrow a .\overrightarrow c } \over {\overrightarrow a .\overrightarrow b }}} \right)\overrightarrow b

Step-by-Step Verified Solution