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VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
MCQ
If $\big|\vec{\text{a}}\times\vec{\text{b}}\big|=4,\big|\vec{\text{a}}.\vec{\text{b}}\big|=2,$ then $|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2=$
  • A
    6
  • B
    2
  • ✓
    20
  • D
    8
✓

Answer

Correct option: C.
20
We know

$\big(\vec{\text{a}}.\vec{\text{b}}\big)^2+\big|\vec{\text{a}}\times\vec{\text{b}}\big|62=|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2\dots(1)$

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

$\Rightarrow\big|\vec{\text{a}}.\vec{\text{b}}\big|^2=\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$

From (1), we get

$(2)^2+(4)^2=|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2$

$\Rightarrow|\vec{\text{a}}|^2\big|\vec{\text{b}}\big|^2=20$

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