Let a - b- and c be three unit vectors such that a - b - c -3-2 b - c -If b is not parallel to c- then the angle betweena and b is -A- -2B- 2 -3C- 5 -D- 5 -3 -4

The correct option is C a× (b×c) = (a.c)b (a.b)c = √(3)/2 (b + c) and after comparing a.b= √(3)/2 ⇒ cos θ = √(3)/2 ⇒θ = 5 π/6 ...

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Byju's Answer

Standard XII

Mathematics

Scalar Triple Product

Let a , b, an...

Question

Let $\to a, \to b, a n d \to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b \times \to c) . I f \to b$ is not parallel to $\to c$ , then the angle between $\to a a n d \to b$ is :

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Solution

The correct option is C

$\to a \times (\to b \times \to c) = (\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\sqrt{3}}{2} (\to b + \to c) and after comparing \to a . \to b = - \frac{\sqrt{3}}{2} \Rightarrow c o s θ = - \frac{\sqrt{3}}{2} \Rightarrow θ = - \frac{5 π}{6}$

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Similar questions

Let $^a,^b a n d^c$ be three unit vectors such that
$^a \times (^b \times^c) = \frac{\sqrt{3}}{2} (^b +^c) .$ If
$^b$ is not parallel to $^c$ , then the angle between $^a$ and $^b$ 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:

a, b, c

are three unit vectors such that

a \times (b \times c) = \frac{1}{2} (b + c)

. If the vectors

b

and

c

are non-parallel, then the angle between

a

and

b

is equal to

Q. If

a, b, c

are three unit vectors such that

a \times (b \times c) = \frac{1}{2} b

and

c

being non parallel, then

Q. If

a, b, c

be three unit vectors such that

a \times (b \times c) = \frac{1}{2} b, b

and

c

being non-parallel. If

θ_{1}

is the angle between

a

c

and

θ_{2}

is the angle between

a

b

, then

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Let →a,→b,and →c be three unit vectors such that →a×(→b×→c)=√32(→b×→c).If →b is not parallel to →c, then the angle between →a and →b is :

The correct option is C →a×(→b×→c)=(→a.→c)→b−(→a.→b)→c=√32(→b+→c)and after comparing→a.→b=−√32⇒cosθ=−√32⇒θ=−5π6

Let $\to a, \to b, a n d \to c$ be three unit vectors such that $\to a \times (\to b \times \to c) = \frac{\sqrt{3}}{2} (\to b \times \to c) . I f \to b$ is not parallel to $\to c$ , then the angle between $\to a a n d \to b$ is :

The correct option is C

$\to a \times (\to b \times \to c) = (\to a . \to c) \to b - (\to a . \to b) \to c = \frac{\sqrt{3}}{2} (\to b + \to c) and after comparing \to a . \to b = - \frac{\sqrt{3}}{2} \Rightarrow c o s θ = - \frac{\sqrt{3}}{2} \Rightarrow θ = - \frac{5 π}{6}$