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,

l^{2} + m^{2} + n^{2} = 1

⇒ l^{2} + l^{2} + l^{2} = 1 [∵ l = m = n]

⇒ 3.l^{2} = 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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