Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).
Practice Questions
1 question
Q1
Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).
3
4
1
0
Scalar projection = (A · B) / |B| = (3*1 + 4*0) / 1 = 3.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).
Solution: Scalar projection = (A · B) / |B| = (3*1 + 4*0) / 1 = 3.
Steps: 5
Step 1: Identify the vectors A and B. Here, A = (3, 4) and B = (1, 0).
Step 2: Calculate the dot product of A and B. This is done by multiplying the corresponding components of the vectors and adding them together: A · B = (3 * 1) + (4 * 0).
Step 3: Simplify the dot product calculation: A · B = 3 + 0 = 3.
Step 4: Calculate the magnitude (length) of vector B. The magnitude |B| is calculated using the formula |B| = sqrt(x^2 + y^2), where B = (1, 0). So, |B| = sqrt(1^2 + 0^2) = sqrt(1) = 1.
Step 5: Finally, find the scalar projection of vector A onto vector B using the formula: Scalar projection = (A · B) / |B|. Substitute the values: Scalar projection = 3 / 1 = 3.
