Project U onto V. U=(4,2) V=(1,-2)
?? Is there a formula for this?
In general
the projection of U onto V is:
(U dot V)/|V|
= (4,2)dot(1,-2)/|V|
= (4-4)/√5
= 0/√5
= 0
makes sense, since the 2 vectors are orthogonal, that is, they form a 90° angle with each other
(their dot product is zero)
Thanks Reiny!!
Yes, there is a formula for projecting one vector onto another. The projection of vector U onto vector V can be calculated using the following formula:
Proj_V_U = (U dot V / ||V||^2) * V
Where:
- U dot V denotes the dot product of U and V.
- ||V|| represents the magnitude (or length) of vector V.
- V is the vector onto which U is being projected.
- Proj_V_U is the projected vector of U onto V.
Now, let's calculate the projection of U onto V using this formula:
Step 1: Calculate the dot product of U and V:
U dot V = (4 * 1) + (2 * -2) = 4 - 4 = 0
Step 2: Calculate the magnitude of V:
||V|| = sqrt(1^2 + (-2)^2) = sqrt(5)
Step 3: Calculate Proj_V_U:
Proj_V_U = (U dot V / ||V||^2) * V
= (0 / (sqrt(5))^2) * (1, -2)
= 0 * (1, -2)
= (0, 0)
Therefore, the projection of U onto V is the zero vector, (0, 0).