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

The correct option is B 1 #160;a⃗, b⃗ #160; #160;are non collinear and hence linearly independent.Thus, #160;αa⃗ + βb⃗ = 0 ⇒α = β = #160;0 ...

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Standard XII

Mathematics

Bijective Function

If a⃗ and ...

Question

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

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Solution

The correct option is B $1$
$\to a, \to b$ are non collinear and hence linearly independent.
Thus,
$α \to a + β \to b = 0 \Rightarrow α = β = 0.$
So,
$2 x - y = 5$ and $x - 2 y = 4$
$∴ 4 x - 2 y = 10, x - 2 y = 4$
$3 x = 6 \Rightarrow x = 2, y = - 1$
$x + y = 1$

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

The correct option is B 1→a,→b are non collinear and hence linearly independent.Thus,α→a+β→b=0⇒α=β=0. So, 2x−y=5 and x−2y=4 ∴4x−2y=10,x−2y=4 3x=6⇒x=2,y=−1 x+y=1

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

The correct option is B $1$
$\to a, \to b$ are non collinear and hence linearly independent.
Thus,
$α \to a + β \to b = 0 \Rightarrow α = β = 0.$
So,
$2 x - y = 5$ and $x - 2 y = 4$
$∴ 4 x - 2 y = 10, x - 2 y = 4$
$3 x = 6 \Rightarrow x = 2, y = - 1$
$x + y = 1$