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Question

A vector r is inclined at equal angles to the three axes.If the magnitude or r is 23 units, then find the value of r .


Solution

We have,     |r|=23

Since,r is equally inclined to the three axes. r so direction cosines of the unit vector r will be same. i.e., l = m = n.

We know that,

    l2+m2+n2=1  l2+l2+l2=1  l2=13  l=±(13)So,   ^r=±13^i±13^j±13^k             r=^r|r|                     [ ^r=r|r|]    =[±13^i±13^j±13^k]23    [  |r|=23]    =±2^i±2^j±2^k=±2(^i+^j+^k)

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