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Section Formula

If D⃗A⃗ =a⃗...

Question

If $\to D A = \to a$ , $\to A B = \to b$ , $\to C B = \to k a$ where $k > 0$ X, Y are the mid points of DB and AC respectively, such that $| \to a | = 17$ and $∣ ∣ \to X Y ∣ ∣ = 4$ , then k equal to ?

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Solution

Let D be origin $\to D A = \to A - \to D = \to a$
$\Rightarrow \to A = \to a$
$\to A B = \to B - \to A = \to b$
$\Rightarrow \to B = \to a + \to b$
$\to C B = \to B - \to C = k \to a$
$\Rightarrow \to C = \to a + \to b - k \to a$
$\to x = \frac{\to a + \to b}{2}$ , $\to y = \frac{2 \to a + \to b - k \to a}{2}$
$\to x y = \frac{\to a - k \to a}{2} = (\frac{1 - k}{2}) \to a$
$(\to x y) = (\frac{1 - k}{2}) | \to a |$
$\Rightarrow 4 = (\frac{1 - k}{2}) 17$
$\Rightarrow 1 - k = \frac{8}{17}$
$\Rightarrow k = \frac{9}{17}$ .

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\to D A = \to a; \to A B = \to b

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Q. ABCD is parallelogram. If

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