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Question

A vector r is inclined at equal acute angles to x-axis, y-axis and z-axis. If r = 6 units, find r.

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Solution

Suppose, vector r makes an angle α with each of the axis OX, OY and OZ. Then, its direction cosines are l = cos α , m = cos α and n = cos α i.e. l = m = n.

Now, l2 + m2 + n2 = 1 l2 + l2 + l2 = 1 3l2 = 1 l2 = 13 l =± 13Since, r makes acute angle with the axis.Hence, we take only positive value.
Therefore,

r = r l i^ + m j^ + n k^ r = 6 13 i^ + 13 j^ + 13 k^ = 23 i^ + j^ + k^


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