If the vector $\vec{b}$ is collinear with the vector $\vec{a} =(2\sqrt{2},-1,4) \:and \:\left | \vec{b} \right |=10, \:then$ Option 1) $\vec{a}+\vec{b}=0$ Option 2) $\vec{a}+\vec{2b}=0$ Option 3) $\vec{2a}\ ^+_-\ \vec{b}=0$ Option 4) None

P Prateek Shrivastava

Use the concept

Magnitude of a Vector -

The length of the directed line segment $\overrightarrow{AB}$ is called its magnitude.

- wherein

It is denoted by $\mid \overrightarrow{AB\mid }$

given that

$\vec{b}=\lambda \left ( 2\sqrt{2}i-j+4k \right )$

$\left | \vec{b} \right |^{2}=8\lambda ^{2}+\lambda ^{2}+16\lambda ^{2}=25\lambda ^{2}$

$=\frac{100}{25}=\lambda ^{2}=4$

$\therefore \lambda =\pm 2$

$\vec{b}=4\sqrt{2}i-2j+8k$

or

$\vec{b}= -2\sqrt{2}i+2i-8k$

$\vec{b}= \pm \underset{2a}{\rightarrow}$

$\therefore \vec{b}\pm 2\vec{a}=0$

Option 1)

$\vec{a}+\vec{b}=0$

Incorrect option

Option 2)

$\vec{a}+\vec{2b}=0$

Incorrect option

Option 3)

$\vec{2a}\ ^+_-\ \vec{b}=0$

Correct option

Option 4)

None

Incorrect option

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