Question

A unit vector perpendicular to vector c and coplanar with vectors a and b is

• A. $\frac { \mathbf { a } \times ( \mathbf { b } \times \mathbf { c } ) } { | \mathbf { a } \times ( \mathbf { b } \times \mathbf { c } ) | }$
• B. $\frac { \mathbf { b } \times ( \mathbf { c } \times \mathbf { a } ) } { | \mathbf { b } \times ( \mathbf { c } \times \mathbf { a } ) | }$
• C. $\frac { \mathbf { c } \times ( \mathbf { a } \times \mathbf { b } ) } { | \mathbf { c } \times ( \mathbf { a } \times \mathbf { b } ) | }$
• D. None of thes

Answer 1

Answer: (C)

$\frac { \mathbf { c } \times ( \mathbf { a } \times \mathbf { b } ) } { | \mathbf { c } \times ( \mathbf { a } \times \mathbf { b } ) | }$

Answer 2

Any vector $( \mathbf { r } )$ in plane of $\mathbf { a } , \mathbf { b }$ must be in form of linear combination of $\mathbf { a }$ and $\mathbf { b }$

$\vec { r } = x \mathbf { a } + y \mathbf { b }$

Such combination is possible in alternate $( c )$

As …..(i)

Also (i) is perpendicular to

As

Thus unit vector perpendicular to and coplanar with $\mathbf { a } , \mathbf { b }$ is, .

Other similar concets :

(1) Unit vector perpendicular to $\mathbf { a }$ and coplanar with $\mathbf { b }$ and is .

(2) Unit vector perpendicular to $\mathbf { b }$ and coplanar with and $\mathbf { a }$ is$\mathbf { r } = \frac { \mathbf { b } \times ( \mathbf { c } \times \mathbf { a } ) } { | \mathbf { b } \times ( \mathbf { c } \times \mathbf { a } ) | }$ .