# If ∣ ∣ → a × → B ∣ ∣ = 4 , ∣ ∣ → a ⋅ → B ∣ ∣ = 2 , Then | → a | 2 ∣ ∣ → B ∣ ∣ 2 = - Mathematics

MCQ

If $\left| \vec{a} \times \vec{b} \right| = 4, \left| \vec{a} \cdot \vec{b} \right| = 2, \text{ then } \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 =$

• 6

• 2

• 20

• 8

#### Solution

$\text{ We know }$

$\left( \vec{a} . \vec{b} \right)^2 + \left| \vec{a} \times \vec{b} \right|^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 . . . (1)$

$\left| \vec{a} . \vec{b} \right| = 2 (\text{ Given } )$

$\Rightarrow \left| \vec{a} . \vec{b} \right|^2 = \left( \vec{a} . \vec{b} \right)^2$

$\text{ From (1), we get }$

$\left( 2 \right)^2 + \left( 4 \right)^2 = \left| \vec{a} \right|^2 \left| \vec{b} \right|^2$

$\Rightarrow \left| \vec{a} \right|^2 \left| \vec{b} \right|^2 = 20$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
MCQ | Q 12 | Page 35