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  • When we multiply a vector <img alt="\vec{A}=2\hat{i}+3\hat{j}-5\hat{k}," src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cvec%7BA%7D%3D2%5Chat%7Bi%7D&plus;3%5Chat%7Bj%7D-5%5Chat%7Bk%7D%2

When we multiply a vector \vec{A}=2\hat{i}+3\hat{j}-5\hat{k}, with a number -2 , we get

Option: 1

A scalar with magnitude same as that of the vector


Option: 2

A vector with same magnitude and opposite direction.


Option: 3

A vector with double mangnitude and opposite direction.


Option: 4

A vector with double magnitude and same direction


Answers (1)

best_answer

As we learned

MULTIPLICATION OF VECTORS BY REAL NUMBERS -

1-(Vector Multiplication) If a vector is multiplied by any scalar (n=1,2,3..) We get again a vector.

\vec{Z}= n\cdot \vec{Y}

Vector \timesScalar= Vector

2-If a vector is multiplied by any real number (eg 2 or -2)  then again, we get a vector quantity.

 

- wherein

If \vec{A} is multiplied by 2 then direction of resultant vector is same as that of given vector.

Vector =2\vec{A}

E.g.

If \vec{A} is multiplied by by (-2), then direction of resultant is opposite to that of given vector.

Vector =-2\vec{A}

 

 

\vec{B}=-2.\vec{A}=2(-\vec{A})

\therefore   Direction of \vec{B} is opposite of \vec{A} and magnitude of \left | \vec{B} \right |=2\times magnitude\; of\; \left | \vec{A} \right | .

So, option 3 is correct

Posted by

Rakesh

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