Question

If and are two non-collinear vectors such that . $( \vec { b } + \vec { c } )$ = 4&× $( \vec { b } \times \vec { c } )$ = (x² – 2x + 6) + (siny) , then the point (x, y) lies on

• A. x = 1
• B. y = 1
• C. y = p
• D. x + y = 0

Answer 1

Answer: (A)

x = 1

Answer 2

$\vec { a } \cdot \vec { b } + \vec { a } \cdot \vec { c }$ = 4 ……..(i) &

= (x² – 2x + 6) $\overrightarrow { \mathrm { b } }$ + (siny) $\overrightarrow { \mathrm { c } }$ Q $\overrightarrow { \mathrm { b } }$ &are non-collinear vectors

Ž= x² – 2x + 6 & $\vec { a } \cdot \vec { b }$ = – siny putting in (i) we get

x² – 2x + 6 – siny = 4

Ž (x – 1)² + (1 – siny) = 0 \ x = 1 & siny = 1