Question

If a, b, c are the three non-coplanar vectors and p, q, r are defined by the relations $\mathbf { p } = \frac { \mathbf { b } \times \mathbf { c } } { [ \mathbf { a } \mathbf { b } \mathbf { c } ] } , \mathbf { q } = \frac { \mathbf { c } \times \mathbf { a } } { [ \mathbf { a } \mathbf { b } \mathbf { c } ] } , \mathbf { r } = \frac { \mathbf { a } \times \mathbf { b } } { [ \mathbf { a } \mathbf { b } \mathbf { c } ] }$ then (a+b) . p +(b+c) . q +(c+a) . r =

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

3

Answer 2

We have $\mathbf { p } \cdot ( \mathbf { a } + \mathbf { b } ) = \mathbf { p } \cdot \mathbf { a } + \mathbf { p } \cdot \mathbf { b }$

$= 1 + 0 = 1$ ,

Similarly, and

Thus, required result is 1+1+1=3.