# If → a and → B Are Unit Vectors, Then Write the Value of ∣ ∣ → a × → B ∣ ∣ 2 + ( → a . → B ) 2 . - Mathematics

Short Note

If $\vec{a} \text{ and } \vec{b}$ are unit vectors, then write the value of $\left| \vec{a} \times \vec{b} \right|^2 + \left( \vec{a} . \vec{b} \right)^2 .$

#### Solution

$\text{ It is given that } \vec{a} \text{ and } \vec{b} \text{ are unit vectors } .$
$\Rightarrow \left| \vec{a} \right| = \left| \vec{b} \right| = 1 . . . (1)$
$\text{ Now } ,$
$\left( \vec{a} . \vec{b} \right)^2 + \left| \vec{a} \times \vec{b} \right|^2$
$= \left( \left| \vec{a} \right| \left| \vec{b} \right| \cos \theta \right)^2 + \left( \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta \right)^2$
$= \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 \left( \cos^2 \theta + \sin^2 \theta \right)$
$= \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 \left( 1 \right)$
$= \left| \vec{a} \right|^2 \left| \vec{b} \right|^2$
$= 1^2 1^2 [\text{ From } (1)]$

= 1

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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
very short answers | Q 21 | Page 34