The unit vector that is in the same direction as v is given by:
The vector is given by the <u>terminal point subtracted by the initial point,</u> hence:
v = (-17, 4) - (7, -9) = <-24, 13>
<h3>How to find the unit version of a vector?</h3>Each coordinate of the vector is <u>divided by it's norm</u>.
For this vector, the norm is given by:
Hence the unit vector is:
More can be learned about vectors at brainly.com/question/24606590
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Answer:
Step-by-step explanation:
In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:
Moving the 9 to the other side since the derivative of a constant is 0 gives us
By implicit differentation, the derivative of that function is
To find the derivative, we have to solve for dy/dx:
Factor out the dy/dx to get:
Now divide to get your slope formula (first derivative):
Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:
So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:
y-y₁ = m(x-x₁)
Filling in we get:
y - 0 = 5/3(x - 5) so the equation of the tangent line is:
Good luck in your calculus class!
