If -x-y-x-y-1- then -x-y-

The correct option is C √(3)|x|=|y|=|x+y|=1 We know that |x+y|^2=|x|^2+|y|^2+2x·y ⇒ 1=1+1+2x·y ⇒x·y= 12 Now, |x y|^2=|x|^2+|y|^2 2x·y ⇒ |x y|^2=1+1+1=3 ∴ |x y ...

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Standard XII

Mathematics

Addition of Vectors

If |x⃗|=|y⃗|=...

Question

If $| \to x | = | \to y | = | \to x + \to y | = 1$ , then $| \to x - \to y | =$ _______

\sqrt{2}

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\sqrt{3}

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Solution

The correct option is B $\sqrt{3}$
$| \to x | = | \to y | = | \to x + \to y | = 1$
We know that
$| \to x + \to y |^{2} = | \to x |^{2} + | \to y |^{2} + 2 \to x \cdot \to y$
$\Rightarrow 1 = 1 + 1 + 2 \to x \cdot \to y$
$\Rightarrow \to x \cdot \to y = - \frac{1}{2}$

Now, $| \to x - \to y |^{2} = | \to x |^{2} + | \to y |^{2} - 2 \to x \cdot \to y$
$\Rightarrow | \to x - \to y |^{2} = 1 + 1 + 1 = 3$
$∴ | \to x - \to y | = \sqrt{3}$

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If |→x|=|→y|=|→x+→y|=1, then |→x−→y|=_______

The correct option is B √3|→x|=|→y|=|→x+→y|=1 We know that |→x+→y|2=|→x|2+|→y|2+2→x⋅→y ⇒1=1+1+2→x⋅→y ⇒→x⋅→y=−12 Now, |→x−→y|2=|→x|2+|→y|2−2→x⋅→y ⇒|→x−→y|2=1+1+1=3 ∴|→x−→y|=√3

If $| \to x | = | \to y | = | \to x + \to y | = 1$ , then $| \to x - \to y | =$ _______