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Applications Scalar Triple Product

If a+b+c=0, |...

Question

If $\to a + \to b + \to c = 0, | \to a | = 3, | \to b | = 5, | \to c | = 7$ , then the angle between $\to a$ and $\to b$ is

A

\frac{5 π}{3}

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B

\frac{π}{6}

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C

\frac{π}{3}

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D

\frac{2 π}{3}

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Solution

The correct option is C $\frac{π}{3}$
$\to a + \to b + \to c = 0, | \to a | = 3, | \to b | = 5, | \to c | = 7$
$(\to a + \to b + \to c)^{2} = 0$
$\Rightarrow | \to a |^{2} + | \to b |^{2} + | \to c |^{2} + 2 (\to a . \to b + \to b . \to c + \to c . \to a) = 0$
$\Rightarrow \to a . \to b + \to b . \to c + \to c . \to a = - \frac{83}{2}$ ... (1)
$\to a . \to a + \to a . \to b + \to a . \to c = 0 \Rightarrow \to a . \to b + \to a . \to c = - 9$ ... (2)
$\to a . \to b + \to b . \to b + \to b . \to c = 0 \Rightarrow \to a . \to b + \to b . \to c = - 25$ ... (3)
$\Rightarrow 2 (\to a . \to b) + \to a . \to c + \to b . \to c = - 34 \Rightarrow \to a . \to b = \frac{15}{2}$
$\Rightarrow$ Angle between $\to a$ and $\to b$ is $\frac{π}{3}$

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Similar questions

a + b + c = 0, | a | = 3, | b | = 5, | c | = 7,

then the angle between a and b is

a + b + c = 0

| a | = 5, | b | = 3

| c | = 7

then angle between

a

b

a + b + c =

0

∣ ∣ \to a ∣ ∣ = 3 ∣ ∣ ∣ \to b ∣ ∣ ∣ = 5

| c | = 7,

, then the angle between

a

b

\to a + \to b + \to c = \to 0

∣ ∣ \to a ∣ ∣ = 3, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 5, ∣ ∣ \to c ∣ ∣ = 7,

then the angle between

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\to b

¯ a + ¯ b + ¯ c = 0

| a | = 3, | b | = 5, | c | = 7

, then the angle between

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