If a- and b- are two vectors such that -a-b-b- then prove that a-2b- is perpendicular to a-

(a) ∵ |a⃗+b⃗|^2=|b⃗|^2 ⇒ ( a⃗+b⃗ ). ( a⃗+b⃗ )=b⃗.b⃗ ⇒a⃗.a⃗+2a⃗.b⃗=0 ⇒a⃗.(a⃗+2b⃗)=0 Hence a⃗⊥ (a⃗+2b⃗) ...

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Vector Addition

If a⃗ and b⃗ ...

Question

If $\to a and \to b$ are two vectors such that $| \to a + \to b | = | \to b |,$ then prove that $(\to a + 2 \to b)$ is perpendicular to $\to a .$

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Solution

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

| \to a | \to b - | \to b | \to a

\to a

\to b

\to a

\to b

\to a + 2 \to b

5 \to a - 4 \to b,

\to a

\to b

\to a

\to b

| \to a + \to b | = | \to a - 2 \to b |

\to a

\to b

\to a + 2 \to b

5 \to a - 4 \to b,

\to a

\to b

\to a

\to b

| \to a + \to b | = \sqrt{3} .

\to c = \to a + 2 \to b + 3 (\to a \times \to b),

2 | \to c |

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