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Vectors and Its Types

If a⃗ , b⃗ ...

Question

If $\to a, \to b, \to c$ be the unit vectors such that $\to b$ is not parallel to $\to c$ and $\to a \times (2 \to b \times \to c) = \to b$ then the angle that $\to a$ makes with $\to b$ and $\to c$ are respectively:

A

\frac{π}{3} & \frac{π}{4}

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B

\frac{π}{3} & \frac{2 π}{3}

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C

\frac{π}{2} & \frac{2 π}{3}

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D

\frac{π}{2} & \frac{π}{3}

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Solution

The correct option is D $\frac{π}{2} & \frac{π}{3}$
$\begin{matrix} (\to a . \to c) 2 \to b - 2 (\to a . \to b) \to c = \to b \to a . \to b = 0 \to a . \to c = \frac{1}{2} N o w, \to a ⊥ \to b \Rightarrow | \to a | | \to c | cos θ = \frac{1}{2} 1 \times 1 cos θ = \frac{1}{2} θ = \frac{π}{3} H e n c e, o p t i o n D i s t h e c o r e c t a n s w e r . \end{matrix}$

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Similar questions

\to a, \to b, \to c

are unit vectors such that

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

(\to a, \to b) = \frac{π}{3}

| \to a \times \to b | + | \to b \times \to c | + | \to c \times \to a | =

\to a, \to b, \to c

be three unit vectors such that

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

\to a

\to c

are non-parallel, then the angles which

\to b

\to c

\to a

are respectively

\to a, \to b

\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) \cdot

\to b

is not parallel to

\to c .

Then the angle between

\to a

\to b

\to a, \to b

\to c

be three unit vector such that

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

\to b

is not parallel to

\to c

. then angle between

\to a

\to b

\to a, \to b, \to c

be three unit vectors such that

∣ ∣ \to a + \to b + \to c ∣ ∣ = 1

\to a ⊥ \to b

\to c

α, β

\to a, \to b

respectively then

cos α + cos β

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