Find the angle between two vectors a and b with magnitudes -3 and 2 respectively such that a - b -6-

The correct option is C π4 Let θ be the angle between a and b . |a|=√(3), |b|=2 and a. b=√(6) Therefore, cosθ = a . b|a||b| ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Angle between Two Lines

Find the angl...

Question

Find the angle between two vectors $\to a$ and $\to b$ with magnitudes $\sqrt{3}$ and $2$ respectively such that $\to a . \to b = \sqrt{6}$ .

\frac{π}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{π}{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{π}{6}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\frac{π}{4}$
Let $θ$ be the angle between $\to a$ and $\to b$ .
$| \to a | = \sqrt{3}, | \to b | = 2$ and $\to a . \to b = \sqrt{6}$
Therefore, $cos θ = \frac{\to a . \to b}{| \to a | | \to b |}$

$cos θ = \frac{\sqrt{6}}{\sqrt{3} \times 2} = \frac{1}{\sqrt{2}} = cos \frac{π}{4}$

$θ = \frac{π}{4}$

Hence, the measure of the angle between $\to a$ and $\to b$ is $\frac{π}{4}$ .

Suggest Corrections

Similar questions

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

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

The angle between two vectors $\to a a n d \to b$ with magnitudes $\sqrt{3}$ and 4, respectively and $\to a . \to b = 2 \sqrt{3}$ is

(a) $\frac{π}{6}$

(b) $\frac{π}{3}$

(d) $\frac{5 π}{2}$

Let the vectors a and b be such that $| a | = 3$ and $| b | = \frac{\sqrt{2}}{3}$ , then $a \times b$ is a unit vector, if the angle between a and b is

a) $\frac{π}{6}$

b) $\frac{π}{4}$

c) $\frac{π}{3}$

d) $\frac{π}{2}$

Q. Find a vector

\to r

of magnitude

3 \sqrt{2}

units which makes and angle

\frac{π}{4}

and

\frac{π}{2}

with

y

and z-axis respectively

Let the angle between vectors $\to a$ and $\to b$ is $\frac{π}{6}$ , between vectors $\to b$ and $\to c$ is $\frac{π}{4}$ and between vectors $\to c$ and $\to a$ is $\frac{π}{3}$ . The angle, the vector $\to a$ makes with the plane containing vectors $\to b$ and $\to c$ , is

Join BYJU'S Learning Program

Find the angle between two vectors →a and →b with magnitudes √3 and 2 respectively such that →a.→b=√6.

The correct option is C π4Let θ be the angle between →a and →b.|→a|=√3,|→b|=2 and →a.→b=√6Therefore, cosθ=→a.→b|→a||→b|cosθ=√6√3×2=1√2=cosπ4θ=π4Hence, the measure of the angle between →a and →b is π4.

Find the angle between two vectors $\to a$ and $\to b$ with magnitudes $\sqrt{3}$ and $2$ respectively such that $\to a . \to b = \sqrt{6}$ .