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A vector \(\vec r\) is inclined at equal angles to the three axes. If the magnitude of \(\vec r\) is 2√3 units, find \(\vec r\).

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Best answer

Given that,

Also, given that

Vector \(\vec r\) is equally inclined to the three axes.

This means, direction cosines of the unit vector \(\vec r\) 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 \(\hat r\) is represented in terms of direction cosines as,

by (10 points)
great explanation!

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