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If a, b, are ...

Question

If a, b, are three vectors such that each is inclined at an angle $π / 3$ with the other two and $| a | = 1, | b | = 2, | c | = 3,$ then the scalar product of the vectors $2 a + 3 b - 5 c$ and $4 a - 6 b + 10 c$ is equal to

A

-334

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B

188

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C

-522

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D

-514

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Solution

The correct option is D -334
$(2 \to a + 3 \to b - 5 \to c) \cdot (4 \to a - 6 \to b + 10 \to c) = 8 \to a - 50 \to c - \to a \cdot \to b + 20 \to a \to c + 12 \to b \cdot \to a + 30 \to b \cdot \to c - 20 \to c \cdot \to a + 30 \to c \cdot \to b = {8 ∣ ∣ \to a ∣ ∣}^{2} - 18 {∣ ∣ ∣ \to b ∣ ∣ ∣}^{2} - 50 {∣ ∣ \to c ∣ ∣}^{2} + 60 \to b \cdot \to c = 8 {(1)}^{2} - 50 {(3)}^{2} + 60 \cdot 2 \cdot 2 cos (\frac{π}{3}) - 18 {(2)}^{2} = - 334$

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Similar questions

\to a, \to b, \to c

are three vectors such that each is inclined at an angle

\frac{π}{3}

with the other two and

| \to a | = 1, | \to b | = 2, | \to c | = 3

, then the scalar product of the vectors

2 \to a + 3 \to b - 5 \to c

4 \to a - 6 \to b + 10 \to c

\to a, \to b, \to c

are three unit vectors, each is inclined at an angle

\frac{π}{3}

with the other, then scalar triple product

[\to a \to b \to c]

\to a, \to b, \to c

are unit vectors equally inclined to each other at an angle

\frac{π}{3}

[\to b + \to c, \to c + \to a, \to a + \to b] =

If $\to a$ , $\to b$ and $\to c$ are three vectors of equal magnitude. The angle between each pair of vectors is $\frac{π}{3}$ such that $∣ ∣ ∣ \to a + \to b + \to c ∣ ∣ ∣ = \sqrt{6}$ . Then | $\to a$ | is equal to

\to a

\to b

are two vectors such that

| \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

, then the angle between

\to b

\to c

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