Q144 / 225 · JEE Main 2002 · Mathematics

$\vec{a}=3 \hat{i}-5 \hat{j}$ and $\vec{b}=6 \hat{i}+3 \hat{j}$ are two vectors and $\vec{c}$ is a vector such that $\vec{c}=\vec{a} \times \vec{b}$ then $$ |\vec{a}|:|\vec{b}|:|\vec{c}| $$

  • A
    $\sqrt{34}: \sqrt{45}: \sqrt{39}$
  • Correct answer
    B
    $\sqrt{34}: \sqrt{45}: 39$
  • C
    $34: 39: 45$
  • D
    $39: 35: 34$

Solution

We have $\vec{a} \times \vec{b}=39 \vec{k}=\vec{c}$ Also $|\vec{a}|=\sqrt{34},|\vec{b}|=\sqrt{45},|\vec{c}|=39 \therefore \quad|\vec{a}|:|\vec{b}|:|\vec{c}|=\sqrt{34}: \sqrt{45}: 39$

Hence, the correct answer is option: 'B'.

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