Can anyone please help me understand the meaning of this question?
So let $f(x,y) = x^2y - 3xy^3 = z$ $P = (1,1,1)$
Equation of tangent plane at $P$: $z = -x-8y+7$
Next the question says 'The unit normal vector at this same point oriented to make an acute angle with the positive $z$ axis is $__$i$+__$j$+__k$
I am not asking for the answer, just an explanation...
Thank you in advance for any help.
By the definition of a plane, there is a unit normal vector, whose direction is oriented in the coefficients of the implicit definition of a plane: $a*x+b*y+c*z = d$
The normal vector would therefore be: $\left<a,b,c\right>$ or a modification thereof (can't recall exactly).
From that, you have the normal vector, and just need to normalize it. $norm(\left<a,b,c\right>)=\frac{\left<a,b,c\right>}{\sqrt{a^2+b^2+c^2}}$
