If a - and b - are two non-collinear unit vectors such that a - b -3- find 2 a -5 b - 3 a - b -

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Dot Product of Two Vectors

If a → and b ...

Question

If $\vec{a} and \vec{b}$ are two non-collinear unit vectors such that $|\vec{a} + \vec{b}| = \sqrt{3},$ find $(2 \vec{a} - 5 \vec{b}) \cdot (3 \vec{a} + \vec{b}) .$

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\vec{a} and \vec{b}

|\vec{a}| = 2, |\vec{b}| = 1 and \vec{a} \cdot \vec{b} = 1,

(3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) .

\to a

\to b

| \to a | = 3

| \to b | = 6

| \to a + \to b | = 7

(3 \to a - 2 \to b) . (2 \to a + 5 \to b - 4 \to a \times \to b)

\vec{a} and \vec{b}

|\vec{a} \times \vec{b}| = 1 and |\vec{a} . \vec{b}| = \sqrt{3}

\vec{a} and \vec{b}

a

b

| a | = 3, | b | = 4

a - b =^i + 2^j + 3^k

{\frac{| a - b |}{| a | | b |}}^{2}

\to a

\to b

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

(2 \to a - 5 \to b) . (3 \to a + \to b) =

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