Let a-b and c be unit vectors- such that a-b-c-x-a-x-1-b-x- 3 2-x-2- Then the angle between x and c is

Let θ be the angle between c and x. Given : nbsp;a+b+c=x Taking dot product of x on both sides, we get a·x+b·x+c·x=|x|^2 ⇒ 1+ 3 2+|c||x|cosθ=4 ⇒ 2cosθ= 32 ⇒θ= ...

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Byju's Answer

Standard IX

Mathematics

Triangle Inequality

Let a,b and c...

Question

Let $\to a, \to b$ and $\to c$ be unit vectors, such that $\to a + \to b + \to c = \to x, \to a \cdot \to x = 1, \to b \cdot \to x = \frac{3}{2}, | \to x | = 2.$ Then the angle between $\to x$ and $\to c$ is

{cos}^{- 1} (\frac{3}{7})

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{cos}^{- 1} (\frac{1}{3})

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{cos}^{- 1} (\frac{3}{4})

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{cos}^{- 1} (\frac{1}{\sqrt{3}})

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Solution

The correct option is C ${cos}^{- 1} (\frac{3}{4})$
Let $θ$ be the angle between $\to c$ and $\to x .$
Given : $\to a + \to b + \to c = \to x$
Taking dot product of $\to x$ on both sides, we get
$\to a \cdot \to x + \to b \cdot \to x + \to c \cdot \to x = | \to x |^{2}$
$\Rightarrow 1 + \frac{3}{2} + | \to c | | \to x | cos θ = 4$
$\Rightarrow 2 cos θ = \frac{3}{2}$
$\Rightarrow θ = {cos}^{- 1} (\frac{3}{4})$

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Similar questions

Q. Let

\to a, \to b a n d \to c

be three unit vectors such that

\to a x (\to b x \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)

. If

\to b

is not parallel to

\to c,

then the angle between

\to a

and

\to b

is :

Q. Let

\to a, \to b

and

\to c

be three unit vectors such that

\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b + \to c)

. If

\to b

is not parallel to

\to c

, then the angle between

\to a

and

\to b

is:

Q. Let

\to x, \to y

and

\to z

be unit vectors such that

\to x + \to y + \to z = \to a, \to x \times (\to y \times \to z) = \to b, (\to x \times \to y) \times \to z = \to c

\to a \cdot \to x = \frac{3}{2}, \to a \cdot \to y = \frac{7}{4}

and

| \to a | = 2

.

Then which of the following option(s) is/are CORRECT ?

Q. Let

\to a

and

\to b

be two vectors such that

| \to a | = 1,

| \to b | = 4

and

\to a \cdot \to b = 2.

\to c

is a vector such that

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

then the angle between

\to b

and

\to c

Q. Let

\to a

and

\to b

be two unit vectors such that

\to a \cdot \to b = 0

. For some

x, y \in R

, let

\to c = x \to a + y \to b + (\to a \times \to b)

. If

| \to c | = 2

and the vector

\to c

is inclined at the same angle

α

to both

\to a

and

\to b

, then the value of

8 {cos}^{2} α

is .

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Let →a,→b and →c be unit vectors, such that →a+→b+→c=→x,→a⋅→x=1,→b⋅→x=32,|→x|=2. Then the angle between →x and →c is

The correct option is C cos−1(34)Let θ be the angle between →c and →x. Given : →a+→b+→c=→x Taking dot product of →x on both sides, we get →a⋅→x+→b⋅→x+→c⋅→x=|→x|2 ⇒1+32+|→c||→x|cosθ=4 ⇒2cosθ=32 ⇒θ=cos−1(34)

Let $\to a, \to b$ and $\to c$ be unit vectors, such that $\to a + \to b + \to c = \to x, \to a \cdot \to x = 1, \to b \cdot \to x = \frac{3}{2}, | \to x | = 2.$ Then the angle between $\to x$ and $\to c$ is