# if then a value of     Option 1) Option 2) 12 Option 3) 24 Option 4)

As we learnt in

Collinear Vectors -

Two vectors are said to be collinear if and only if there exists a scalar m such as that $\vec{a}=m\vec{b}$

- wherein

m is a Scalar.

$\vec{c}\times (\vec{i}+\vec{2j}+\vec{5k})=\vec{0}$

$So\:\vec{c}\:and (\vec{i}+\vec{2j}+\vec{5k})\:are\:collinear$

$\vec{c}=P(\vec{i}+\vec{2j}+\vec{5k})$

$\left |\vec{c} \right |^{2}=P^{2}\times (1^{2}+2^{2}+5^{2})=60\Rightarrow P^{2}=2$

$value= \vec{c}.(-7\vec{i}+2\vec{j}+3\vec{k})$

$=\sqrt{2}(\vec{i}+2\vec{j}+5\vec{k}).(-7\vec{i}+2\vec{j}+3\vec{k})$

$=\sqrt{2}(-7+4+15)=12\sqrt{2}$

Correct option is 4.

Option 1)

This option is incorrect

Option 2)

12

This option is correct

Option 3)

24

This option is incorrect

Option 4)

This option is  incorrect

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