Find the projection of vector A = (2, 3) onto vector B = (1, 1).
Practice Questions
1 question
Q1
Find the projection of vector A = (2, 3) onto vector B = (1, 1).
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Projection of A onto B = (A · B) / |B|^2 * B; A · B = 2*1 + 3*1 = 5; |B|^2 = 1^2 + 1^2 = 2; Projection = (5/2)(1, 1) = (2.5, 2.5).
Questions & Step-by-step Solutions
1 item
Q
Q: Find the projection of vector A = (2, 3) onto vector B = (1, 1).
Solution: Projection of A onto B = (A · B) / |B|^2 * B; A · B = 2*1 + 3*1 = 5; |B|^2 = 1^2 + 1^2 = 2; Projection = (5/2)(1, 1) = (2.5, 2.5).
Steps: 6
Step 1: Identify the vectors A and B. Here, A = (2, 3) and B = (1, 1).
Step 2: Calculate the dot product of A and B, denoted as A · B. This is done by multiplying the corresponding components of A and B and then adding them together: A · B = 2*1 + 3*1 = 2 + 3 = 5.
Step 3: Calculate the magnitude squared of vector B, denoted as |B|^2. This is done by squaring each component of B and adding them: |B|^2 = 1^2 + 1^2 = 1 + 1 = 2.
Step 4: Use the formula for the projection of A onto B: Projection of A onto B = (A · B) / |B|^2 * B.
Step 5: Substitute the values we calculated into the formula: Projection = (5 / 2) * (1, 1).
