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Question
The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hat"i" + 2/sqrt(14)hat"j" + 3/sqrt(14)hat"k"`.
Options
True
False
Solution
This statement is True.
Explanation:
Given plane is x + 2y + 3z – 6 = 0
Vector normal to the plane `vec"n" = hat"i" + 2hat"j" + 3hat"k"`
∴ `hat"n" = vec"n"/|vec"n"|`
= `(hat"i" + 2hat"j" + 3hat"k")/sqrt((1)^2 + (2)^2 + (3)^2`
= `1/sqrt(14)hat"i" + 2/sqrt(14)hat"j" + 3/sqrt(14)hat"k"`
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