If veca and vecb are non zero, non collinear vectors, and the linear combination (2 x-y) veca+4 vecb=5 veca+(x-2 y) vecb holds for real x and y then x+y has the value equal to

Question

If veca and vecb are non zero, non collinear vectors, and the linear combination (2 x-y) veca+4 vecb=5 veca+(x-2 y) vecb holds for real x and y then x+y has the value equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(2 x-y-5) veca =(x-2 y-4) vecb ∴ 2 x-y=5 ...(1) x-2 y=4 ...(2) from (1) and (2) 2(2 y+4)-y=5 ⇒ 3 y=-3 ⇒ y=-1 and x=2 ; hence x+y=1 ⇒ y=-1

Q. If $a$ and $b$ are non zero, non collinear vectors, and the linear combination $(2 x - y) a + 4 b = 5 a + (x - 2 y) b$ holds for real $x$ and $y$ then $x + y$ has the value equal to

$(2 x - y - 5) a$
$= (x - 2 y - 4) b$
$∴ 2 x - y = 5$ ...(1)
$x - 2 y = 4$ ...(2)
from (1) and (2)
$2 (2 y + 4) - y = 5$
$\Rightarrow 3 y = - 3$
$\Rightarrow y = - 1$
and $x = 2;$
hence $x + y = 1$
$\Rightarrow y = - 1$

Q. If a and b are non zero, non collinear vectors, and the linear combination (2x−y)a+4b=5a+(x−2y)b holds for real x and y then x+y has the value equal to

(2x−y−5)a =(x−2y−4)b ∴2x−y=5 ...(1) x−2y=4 ...(2) from (1) and (2) 2(2y+4)−y=5 ⇒3y=−3 ⇒y=−1 and x=2; hence x+y=1 ⇒y=−1

Q. If $a$ and $b$ are non zero, non collinear vectors, and the linear combination $(2 x - y) a + 4 b = 5 a + (x - 2 y) b$ holds for real $x$ and $y$ then $x + y$ has the value equal to

$(2 x - y - 5) a$
$= (x - 2 y - 4) b$
$∴ 2 x - y = 5$ ...(1)
$x - 2 y = 4$ ...(2)
from (1) and (2)
$2 (2 y + 4) - y = 5$
$\Rightarrow 3 y = - 3$
$\Rightarrow y = - 1$
and $x = 2;$
hence $x + y = 1$
$\Rightarrow y = - 1$