What is the projection of vector a = (3, 4) onto vector b = (1, 0)?
Practice Questions
Q1
What is the projection of vector a = (3, 4) onto vector b = (1, 0)?
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Questions & Step-by-Step Solutions
What is the projection of vector a = (3, 4) onto vector b = (1, 0)?
Step 1: Identify the vectors. We have vector a = (3, 4) and vector b = (1, 0).
Step 2: Calculate the dot product of vectors a and b. This is done by multiplying the corresponding components and adding them together: a · b = 3*1 + 4*0 = 3 + 0 = 3.
Step 3: Calculate the magnitude squared of vector b. The magnitude of b = (1, 0) is calculated as |b| = sqrt(1^2 + 0^2) = sqrt(1) = 1. Therefore, |b|^2 = 1^2 = 1.
Step 4: Use the formula for projection. The projection of vector a onto vector b is given by: Projection = (a · b / |b|^2) * b.
Step 5: Substitute the values into the formula: Projection = (3 / 1) * (1, 0).
