A-b-c-0- such that -a-3- -b-5 and -c-7-Find cosine of the angle between b- and c-

The correct option is D 1314 Given #160; a⃗+b⃗+c⃗=0 ——(1) | a⃗ |=3 | b⃗ |=5 | c⃗ |=7 b⃗+c⃗= a⃗ on squaring both sides (b⃗+c⃗ ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

a⃗+b⃗+c⃗=0⃗ s...

Question

$\to a + \to b + \to c = \to 0$ such that $| \to a | = 3, | \to b | = 5$ and $| \to c | = 7$ .

Find cosine of the angle between $\to b$ and $\to c .$

\frac{11}{2}

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\frac{13}{14}

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\frac{- 11}{12}

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\frac{- 13}{14}

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Solution

The correct option is D $\frac{- 13}{14}$
Given

$\to a + \to b + \to c = 0$ ------(1)

$| \to a | = 3$

$∣ ∣ \to b ∣ ∣ = 5$

$| \to c | = 7$

$\to b + \to c = - \to a$

on squaring both sides

$(\to b + \to c)^{2} = (- \to a)^{2}$

$\Rightarrow {∣ ∣ \to b ∣ ∣}^{2} + {| \to c |}^{2} + 2 \to b \cdot \to c = {| \to a |}^{2}$

$\Rightarrow 5^{2} + 7^{2} + 2 ∣ ∣ \to b ∣ ∣ | \to c | cos θ = 3^{2}$

$\Rightarrow 25 + 49 + 2 \times 5 \times 7 cos θ = 9$

$\Rightarrow 2 \times 5 \times 7 cos θ = - 65$

$\Rightarrow 2 \times 7 cos θ = - 13$

$\Rightarrow cos θ = \frac{- 13}{14}$

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Similar questions

Q. If

a, b

and

c

are vectors such that

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

and

| \to a | = 7, | \to b | = 5

and

| \to c | = 3

, then angle between

\to b

and

\to c

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

such that

| \to a | = 3, | \to b | = 5

and

| \to c | = 7

What is the angle between

\to a

and

\to b

Q. For any three vectors

\to a, \to b

and

\to c

, prove that

[\to a + \to b, \to b + \to c, \to c + \to a] = 2 [\to a \to b \to c]

. Hence prove that the vectors

\to a + \to b, \to b + \to c, \to c + \to a

are coplanar. If and only if

\to a, \to b, \to c

are coplanar.

\to a, \to b, \to c

are three non-collinear vectors such that

\to a + \to b

is parallel to

\to c

and

\to a + \to c

is parallel to

\to b

then:

Q. If

\to a, \to b, \to c

and

\to d

are unit vectors such that

(\to a \times \to b) . (\to c \times \to d) = λ

and

\to a . \to c = \frac{\sqrt{3}}{2}

, then

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→a+→b+→c=→0 such that |→a|=3,|→b|=5 and |→c|=7.Find cosine of the angle between →b and →c.

$\to a + \to b + \to c = \to 0$ such that $| \to a | = 3, | \to b | = 5$ and $| \to c | = 7$ .

Find cosine of the angle between $\to b$ and $\to c .$