# If | → a | = 2 , ∣ ∣ → B ∣ ∣ = 7 and → a × → B = 3 ^ I + 2 ^ J + 6 ^ K , Find the Angle Between → a and → B . - Mathematics

Sum

if $\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 7 \text{ and } \vec{a} \times \vec{b} = 3 \hat{ i } + 2 \hat{ j } + 6 \hat{ k } ,$  find the angle between  $\vec{a} \text{ and } \vec{b} .$

#### Solution

$\text{ Let } \theta \text{ be the angle between } \vec{a} \text{ and } \vec{b} .$
$\vec{a} \times \vec{b} = 3 \hat{ i } + 2 \hat{ j } + 6 \hat{ k } (\text{ Given } )$
$\Rightarrow \left| \vec{a} \times \vec{b} \right| = \sqrt{9 + 4 + 36}$
$= 7$
$\text{ We know }$
$\left| \vec{a} \times \vec{b} \right| = \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta$
$\Rightarrow 7 = \left( 2 \right) \left( 7 \right) \sin \theta$
$\Rightarrow \sin \theta = \frac{1}{2}$
$\Rightarrow \theta = \frac{\pi}{6}$

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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
Exercise 25.1 | Q 16 | Page 30