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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

 

Answers (1)

best_answer

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

Posted by

prateek

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