Let a and b are two non-collinear vectors then for which value of x and y 2 u - v- - w- will be true-where u - x a- - 2 y b- - v- - - 2 y a- - 3 x b- and w- -4 a- - 2 b- is

The correct option is A x = 107 , y = 47 u⃗=xa⃗+2yb⃗ v⃗= 2ya⃗+3xb⃗ w⃗=4a⃗ 2b⃗ 2u⃗ v⃗=w⃗ ⇒ 2(xa⃗+2yb⃗) ( 2ya⃗+3xb⃗)=4a⃗ 2b⃗ ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

Let a and ...

Question

Let $\to a$ and $\to b$ are two non-collinear vectors then for which value of $x$ and $y$
$2 \to u - \to v = \to w$ will be true,where $\to u = x \to a + 2 y \to b$ , $\to v = - 2 y \to a + 3 x \to b$ and $\to w = 4 \to a - 2 \to b$ is

x = \frac{4}{7}, y = \frac{6}{7}

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x = \frac{10}{7}, y = \frac{4}{7}

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x = \frac{8}{7}, y = \frac{2}{7}

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x = 2, y = 3

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Solution

The correct option is A $x = \frac{10}{7}, y = \frac{4}{7}$
$\to u = x \to a + 2 y \to b$
$\to v = - 2 y \to a + 3 x \to b$
$\to w = 4 \to a - 2 \to b$
$2 \to u - \to v = \to w$
$\Rightarrow 2 (x \to a + 2 y \to b) - (- 2 y \to a + 3 x \to b) = 4 \to a - 2 \to b$
$\Rightarrow \to a (2 x + 2 y) + \to b (4 y - 3 x) = 4 \to a - 2 \to b$
Comparing coeff. of $\to a$ & $\to b$
$2 x + 2 y = 4$ _ (1)
$4 y - 3 x = - 2$ _ (2)
$\Leftrightarrow x + y = 2$ _ $(1) \times 4$
$3 x - 4 y = 2$ _ (2)
__________________
$7 x = 10$ $\Rightarrow x = 10 / 7$
$y = 4 / 7$

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Let →a and →b are two non-collinear vectors then for which value of x and y 2→u−→v=→w will be true,where →u=x→a+2y→b , →v=−2y→a+3x→b and →w=4→a−2→b is

Let $\to a$ and $\to b$ are two non-collinear vectors then for which value of $x$ and $y$
$2 \to u - \to v = \to w$ will be true,where $\to u = x \to a + 2 y \to b$ , $\to v = - 2 y \to a + 3 x \to b$ and $\to w = 4 \to a - 2 \to b$ is