Q. 65.0( 3 Votes )

A vector is inclined at equal angles to the three axes. If the magnitude of is units, find .

Answer :

Given that,

Magnitude of = 2√3



Also, given that


Vector is equally inclined to the three axes.


This means, direction cosines of the unit vector will be same. The direction cosines are (l, m, n).


l = m = n


The direction cosines of a vector are simply the cosines of the angles between the vector and the three coordinate axes.


We know the relationship between direction cosines is,


l2 + m2 + n2 = 1


l2 + l2 + l2 = 1 [ l = m = n]


3.l2 = 1




Also, we know that is represented in terms of direction cosines as,




We are familiar with the formula,



To find ,



Substituting values of and .





Thus, the value of is .


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