Use the following vectors to answer the question.
u: <-1,7>
v: <6,4>
What is the projection of u onto v?
To find the projection of vector u onto vector v, we can use the formula:
projv(u) = (u · v / ||v||^2) * v
First, let's calculate the dot product of u and v:
u · v = (-1)*(6) + (7)*(4) = -6 + 28 = 22
Next, let's calculate the squared magnitude of vector v:
||v||^2 = (6)^2 + (4)^2 = 36 + 16 = 52
Now, we can substitute these values into the projection formula:
projv(u) = (22 / 52) * v
Simplifying, we get:
projv(u) = (11 / 26) * <6, 4>
Now we can calculate the projection:
projv(u) = <11/26 * 6, 11/26 * 4> = <66/26, 44/26> = <33/13, 22/13>
Therefore, the projection of vector u onto vector v is <33/13, 22/13>.