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

Option 1)
$\sqrt{34}:\sqrt{45}:\sqrt{39}$

Option 2)
$\sqrt{34}:\sqrt{45}:39$

Option 3)
$34:39:45$

Option 4)
$39:35:34$

Answers (1)

best_answer

As we learnt in

Vector Product of two vectors(cross product) -

If $\vec{a}$ and $\vec{b}$ are two vectors and $\Theta$ is the angle between them , then $\vec{a}\times \vec{b}=\left |\vec{a} \left | \right |\vec{b} \right |Sin\Theta \hat{n}$

- wherein

$\hat{n}$ is unit vector perpendicular to both $\vec{a} \: and \: \vec{b}$

$\vec{a}\times \vec{b}\:=\:39\vec{k}\:=\:\vec{c}$

$\left | \vec{a} \right |\:=\:\sqrt{34}\:;\:\left | \vec{b} \right |\:=\:\sqrt{45}\:;\:\left | \vec{c} \right |\:=\:39$

Ratio = $\sqrt{34}:\sqrt{45}:39$

Option 1)

$\sqrt{34}:\sqrt{45}:\sqrt{39}$

This option is incorrect.

Option 2)

$\sqrt{34}:\sqrt{45}:39$

This option is correct.

Option 3)

$34:39:45$

This option is incorrect.

Option 4)

$39:35:34$

This option is incorrect.

Posted by

divya.saini

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