Find the projection of vector A=i-2j+k onto the direction of vector B=4i-4j+7k
find the projection of vector A =i-2j+k onto B =4i-4j+7k
To find the projection of vector A onto the direction of vector B, you can use the formula:
Projection of A onto B = (A · B) / |B|
Where:
- (A · B) denotes the dot product between vector A and vector B.
- |B| represents the magnitude of vector B.
1. Calculate the dot product between vectors A and B:
A · B = (Ai + Bj + Ck) · (Di + Ej + Fk)
= (A * D) + (B * E) + (C * F)
In this case, A = 1, B = -2, C = 1, D = 4, E = -4, F = 7.
So, A · B = (1 * 4) + (-2 * -4) + (1 * 7)
2. Determine the magnitude of vector B:
|B| = √(Bx^2 + By^2 + Bz^2)
In this case, B = 4i - 4j + 7k.
So, |B| = √(4^2 + (-4)^2 + 7^2)
3. Substitute the values into the projection formula:
Projection of A onto B = (A · B) / |B|
Once you perform these calculations, you will obtain the projection of vector A onto the direction of vector B.