Vector Algebra Question 148
Question: Let the value of $ \mathbf{p}=(x+4y),\mathbf{a}+(2x+y+1),\mathbf{b} $ and $ \mathbf{q}=(y-2x+2),\mathbf{a}+(2x-3y-1),\mathbf{b}, $ where a and b are non-collinear vectors. If $ 3\mathbf{p}=2\mathbf{q}, $ then the value of x and y will be
[RPET 1984; MNR 1984]
Options:
A) - 1, 2
B) 2, - 1
C) 1, 2
D) 2, 1
Show Answer
Answer:
Correct Answer: B
Solution:
- Here, $ 3\mathbf{p}=(3x+12y),\mathbf{a}+(6x+3y+3)\mathbf{b} $
$ 2\mathbf{q}=(2y-4x+4),\mathbf{a}+(4x-6y-2),\mathbf{b} $
On comparing, we get $ 3x+12y=2y-4x+4 $
Þ $ 7x+10y=4 $ -..(i)
and $ 2x+9y=-5 $ -..(ii)
On solving equations, we get $ x=2,-1. $
BETA
