If a -b and c are vectors such that a-b - 0 and a -b -c- then

Given : a·b = 0 a +b =c Squaring both sides, (a +b)^2 =c^2 (a +b)· (a +b) nbsp; = |c| ^2 a·a + a·b + nbsp;b· nbsp;a +b· nbsp;b nbsp; = |c| ^2 |a| ^2 + ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to be on the Same Plane

If a ,b and c...

Question

If $\to a, \to b$ and $\to c$ are vectors such that $\to a \cdot \to b = 0$ and $\to a + \to b = \to c,$ then

| \to a |^{2} + | \to b |^{2} = | \to c |^{2}

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| \to b | + | \to c | = | \to a |

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| \to a |^{2} + | \to c |^{2} = | \to b |^{2}

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| \to b |^{2} + | \to c |^{2} = | \to a |^{2}

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Solution

The correct option is A $| \to a |^{2} + | \to b |^{2} = | \to c |^{2}$
Given : $\to a \cdot \to b = 0$
$\to a + \to b = \to c$
Squaring both sides,
$(\to a + \to b)^{2} = {\to c}^{2}$
$(\to a + \to b) \cdot (\to a + \to b) = | \to c |^{2}$
$\to a \cdot \to a + \to a \cdot \to b + \to b \cdot \to a + \to b \cdot \to b = | \to c |^{2}$
$| \to a |^{2} + 0 + 0 + | \to b |^{2} = | \to c |^{2}$
$∴ | \to a |^{2} + | \to b |^{2} = | \to c |^{2}$

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If →a,→b and →c are vectors such that →a⋅→b=0 and →a+→b=→c, then

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If $\to a, \to b$ and $\to c$ are vectors such that $\to a \cdot \to b = 0$ and $\to a + \to b = \to c,$ then