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CBSE Class 12 Math 2008 Solved Paper

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Question : 8 of 29
Marks: +1, -0
Find a unit vector in the direction of a⃗\vec{a} = 3i^−2j^+6k^\hat{3i} - \hat{2j} + \hat{6k}
Solution:  
The unit vector (a^)(\hat{a}) in the direction of a⃗\vec{a} is given by a⃗∣a⃗∣\frac{\vec{a}}{\left|\vec{a}\right|}
a^\hat{a} = 3i^−2j^+6k^32+(−2)2+62\frac{\hat{3i}-\hat{2j}+\hat{6k}}{\sqrt{3^2+(-2)^2+6^2}}
= 3i^−2j^+6k^9+4+36\frac{\hat{3i}-\hat{2j}+\hat{6k}}{\sqrt{9+4+36}}
3i^−2j^+6k^49\frac{\hat{3i}-\hat{2j}+\hat{6k}}{\sqrt{49}}
= 17\frac{1}{7} [3i^−2j^+6k^\hat{3i} - \hat{2j} + \hat{6k}]
= 37i^−27j^+67k^\frac{3}{\hat{7i}} - \frac{2}{\hat{7j}} + \frac{6}{\hat{7k}}
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