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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