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Representation of Vectors

Let the vecto...

Question

Let the vectors and be such that and, then is a unit vector, if the angle between and is

(A) (B) (C) (D)

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Solution

It is given that.

We know that, where is a unit vector perpendicular to both and and θ is the angle between and.

Now, is a unit vector if.

Hence, is a unit vector if the angle between and is.

The correct answer is B.

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Similar questions

Let and be two unit vectors andθ is the angle between them. Then is a unit vector if

(A) (B) (C) (D)

\to a, \to b, \to c

are unit vectors and the angles between

\to a, \to b

\to b, \to c

\to c, \to a

\frac{π}{6}, \frac{π}{3}

\frac{π}{4}

respectively, then

| \to a + \to b + \to c |

\to a, \to b, \to c

be three non-zero vectors such that

\to c

is a unit vectors perpendicular is both

\to a

\to b

. If the angle between

\to a

\to b

\frac{π}{6}

[\to a \to b \to c]^{2} = \frac{1}{4} | \to a |^{2} | \to b |^{2}

\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 vectors such that

| \to a | = \sqrt{3}, | \to b | = 5, \to b . \to c = 10

and the angle between

\to b

\to c

\frac{π}{3} .

\to a

is perpendicular to vector

\to b \times \to c

| \to a \times (\to b \times \to c) |

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