If -a - b- - -a-b- prove that a and b are perpendicular-

Given | a + b #160;| =| a b #160;| Square on both sides | a + b #160;| #160;^ 2 =| a b #160;| #160;^ 2 cos( a , b ...

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Applications of Dot Product

If |a + b| ...

Question

If $∣ ∣ ∣ \to a + \to b ∣ ∣ ∣ = ∣ ∣ ∣ \to a - \to b ∣ ∣ ∣$ , prove that $\to a$ and $\to b$ are perpendicular.

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Solution

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∣ ∣ ∣ \to a + \to b ∣ ∣ ∣ = ∣ ∣ ∣ \to a - \to b ∣ ∣ ∣,

\to a

\to b

Prove that $(a + b) . (a + b) = | a |^{2} + | b |^{2}$ , if and only if a, b are perpendicular, given $a \neq 0$ , $b \neq 0$

\to a

\to b

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

2 \to a + \to b

\to b

\vec{a}

\vec{b}

|\vec{a} + \vec{b}| = |\vec{b}|

\vec{a} + 2 \vec{b}

\vec{a}

\to a, \to b and \to c i f \to a \times \to b = \to c a n d \to a \times \to c = \to b

\to a, \to b a n d \to c

| \to b | = | \to a | a n d | \to a | = 1

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