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If\:\vec{a} = \vec{2i}+\vec{5j}\: and\: \vec{b}= \vec{2i}-\vec{j}

then unit vector in the direction of \vec{a}+ \vec{b} is

  • Option 1)

    \vec{i}+\vec{j}

  • Option 2)

    \sqrt2(\vec{i}+\vec{j})

  • Option 3)

    \frac{(\vec{i}+\vec{j})}{\sqrt2}

  • Option 4)

    \frac{(\vec{i}-\vec{j})}{\sqrt2}

 

Answers (1)

use the concept of

Unit vector -

A vector of unit magnitude in direction of a vector \vec{a} is called unit vector along \widehat{a}.

- wherein

It is denoted by \widehat{a}.

 

 \vec{a}=2i+5j

\vec{b}=2i-j

\vec{a}+\vec{b}=4i+4j

\frac{\vec{a}+\vec{b}}{\left | \vec{a}+\vec{b}\right |}= \frac{4\left ( i+j \right )}{4\sqrt{2}}= \frac{i+j}{\sqrt{2}}

 


Option 1)

\vec{i}+\vec{j}

Incorrect option

Option 2)

\sqrt2(\vec{i}+\vec{j})

Incorrect option

Option 3)

\frac{(\vec{i}+\vec{j})}{\sqrt2}

Correct option

Option 4)

\frac{(\vec{i}-\vec{j})}{\sqrt2}

Incorrect option

Posted by

Vakul

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