Vector Algebra Question 106
Question: Given that the vectors $ \overline{\alpha } $ and $ \overset{\to }{\mathop{\beta }}, $ are non-collinear. The values of x and y for which $ \overset{\to }{\mathop{u}},-\overset{\to }{\mathop{v}},=\overset{\to }{\mathop{w}}, $ holds true if $ \overset{\to }{\mathop{u}},=2x\overset{\to }{\mathop{\alpha }},+y\overset{\to }{\mathop{\beta }},,\overset{\to }{\mathop{v}},=2,y\overset{\to }{\mathop{\alpha }},+3x\overset{\to }{\mathop{\beta }}, $ and $ \overset{\to }{\mathop{w}},=2\overset{\to }{\mathop{\alpha }},-5\overset{\to }{\mathop{\beta }}, $ are
Options:
A) $ x=2,y=1 $
B) $ x=1,y=2 $
C) $ x=-2,y=1 $
D) $ x=-2,y=-1 $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] $ \overset{\to }{\mathop{u}},-\overset{\to }{\mathop{v}},=\overset{\to }{\mathop{w}}, $ $ ( 2x\overset{\to }{\mathop{\alpha }},+y\overset{\to }{\mathop{\beta }}, )-( 2y\overset{\to }{\mathop{\alpha }},+3x\overset{\to }{\mathop{\beta }}, )=2\overset{\to }{\mathop{\alpha }},-5\overset{\to }{\mathop{\beta }}, $ $ (2x-2y)\overset{\to }{\mathop{\alpha }},+(y-3x)\overset{\to }{\mathop{\beta }},=2\overset{\to }{\mathop{\alpha }},-5\overset{\to }{\mathop{\beta }}, $
$ \therefore 2x-2y=2…(i) $ and $ 3x-y=-5…(ii) $ Solving equations (i) and (ii), we get $ x=2 $ and $ y=1 $
BETA
