If u=(0,2,3) and v=(1,3,-1) find the projection of u onto v
a) 1/3 u
b) 3/11 v-> ->
c) (1,1,-1)
d) (1/3, 1, -1/3)
To find the projection of vector u onto vector v, you can use the formula:
Projv(u) = (u · v) / ||v||² * v
Here's how you can apply this formula to find the projection of u onto v:
1. Calculate the dot product of u and v: (0)(1) + (2)(3) + (3)(-1) = -1
2. Calculate the magnitude (length) of vector v: ||v|| = √((1)² + (3)² + (-1)²) = √(1 + 9 + 1) = √11
3. Substitute the values into the formula:
Projv(u) = (-1) / (√11)² * (1, 3, -1)
4. Simplify the expression:
Projv(u) = -1 / 11 * (1, 3, -1) = (-1/11, -3/11, 1/11)
Therefore, the projection of u onto v is option (d) (1/3, 1, -1/3).