Q. 13.5( 2 Votes )

The vector in the direction of the vector that has magnitude 9 is
A.

B.

C.

D.

Answer :

Given is the vector .


Let this vector be , such that



Let us first find the unit vector in the direction of this vector .


We know that, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.


To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector.


Unit vector in the direction of the vector is given as,



As, we have .


Then,



[ if


]





Therefore,



[ and ]


We have found unit vector in the direction of the vector , but we need to find the unit vector in the direction of but also with the magnitude 9.


We have the formula:


Vector in the direction ofwith a magnitude of 9



And as just found.


So,


Vector in the direction ofwith a magnitude of 9=



Thus, vector in the direction of vector and has magnitude 9 is .

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