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

Given: | a⃗ +b⃗ |^2= | a⃗ |^2 | a⃗ |^2+2.a⃗.b⃗+ | b⃗ |^2= | a⃗ |^2 2a⃗.b⃗+b⃗.b⃗=0 (2a⃗+b⃗).b⃗=0 Therefore, 2a⃗+b⃗⊥b⃗ . ...

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Applications of Dot Product

If a and ...

Question

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

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\vec{a}

\vec{b}

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

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

\vec{a}

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

\to a

\to b

\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

\vec{a} and \vec{b}

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

|\overset{⇀}{a} - \overset{⇀}{b}|______________________.

¯ ¯ ¯ a

¯ ¯ b

¯ ¯ ¯ a . ¯ ¯ b < 0

| ¯ ¯ ¯ a . ¯ ¯ b | = | ¯ ¯ ¯ a \times ¯ ¯ b |

¯ ¯ ¯ a

¯ ¯ b

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