If two vectors a - and b - are such that a -2- b -1 and a - b -1- then find the value of 3 a -5 b - 2 a -7 b -

Given #160;thata #8594;=2, #160;b #8594;=1 #160;and #160; #160;a #8594;. #160;b #8594;=1 #160;... #160;1Now,3a #8594; 5b #8594;.2a ...

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Selecting Consecutive Terms in A.P

If two vector...

Question

If two vectors $\vec{a} and \vec{b}$ are such that $|\vec{a}| = 2, |\vec{b}| = 1 and \vec{a} \cdot \vec{b} = 1,$ then find the value of $(3 \vec{a} - 5 \vec{b}) \cdot (2 \vec{a} + 7 \vec{b}) .$

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\vec{a} and \vec{b}

|\vec{a} + \vec{b}| = \sqrt{3},

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

\to a

\to b

∣ ∣ ∣ 2 \to a + 3 \to b ∣ ∣ ∣ = ∣ ∣ ∣ 3 \to a + \to b ∣ ∣ ∣

\to a

\to b

60^{\circ} .

\frac{1}{8} \to a

∣ ∣ ∣ \to b ∣ ∣ ∣

\to a

\to b

| \to a + \to b | = 1

| \to a - \to b |

\to a

\to b

| \to a | = 1, | \to b | = 4, | \to c |^{2} = 192

\to a . \to b = 2

\to c = (2 \to a \times \to b) - 3 \to b

\to b

\to c

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