If R- - A- - B- Show that R2 - A2 - B2 - 2 AB cos -

| R #160; | #160; ^ 2 = R .R | R #160; | #160; ^ 2 =( A + B ).( A + B ) | R #160; | #160; ^ 2 = A . A + A . B + B . A + ...

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Addition of Vectors

If R⃗ = A⃗ ...

Question

If $\to R = (\to A + \to B),$ Show that $R^{2} = A^{2} + B^{2} + 2 A B c o s θ$

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Solution

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\to A + \to B = \to R

A^{2} + B^{2} = R^{2}

\to A

\to B

\to r \times \to a = \to b \times \to a; \to r \times \to b = \to a \times \to b; \to a \neq 0, \to b \neq 0, \to a \neq λ \to b; \to a

\to b

\to r =

\to r \times \to a = \to b, \to r . \to a = 1,

\to r = \to a + \to a \times \to b .

\to r \times \to a = \to b

\to r = \to a \times \to b

\to a = \to i + \to j

\to b = 2 \to j - \to k

\to r \times \to a = \to b \times \to a

\to r \times \to b = \to a \times \to b

\frac{\to r}{| \to r |}

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

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