What is the scalar projection of vector (3, 4) onto (1, 0)?

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Question: What is the scalar projection of vector (3, 4) onto (1, 0)?

Options:

Correct Answer: 3

Solution:

Scalar projection = (3*1 + 4*0) / √(1^2) = 3

What is the scalar projection of vector (3, 4) onto (1, 0)?

What is the scalar projection of vector (3, 4) onto (1, 0)?

Step 1: Identify the two vectors. The first vector is (3, 4) and the second vector is (1, 0).
Step 2: Calculate the dot product of the two vectors. This is done by multiplying the corresponding components and adding them together: (3 * 1) + (4 * 0).
Step 3: Simplify the dot product calculation: 3 * 1 = 3 and 4 * 0 = 0, so the dot product is 3 + 0 = 3.
Step 4: Calculate the magnitude (length) of the second vector (1, 0). The magnitude is found using the formula √(x^2 + y^2), which in this case is √(1^2 + 0^2).
Step 5: Simplify the magnitude calculation: 1^2 = 1 and 0^2 = 0, so the magnitude is √(1 + 0) = √1 = 1.
Step 6: Finally, calculate the scalar projection using the formula: scalar projection = dot product / magnitude. This means we take the dot product (3) and divide it by the magnitude (1).
Step 7: Simplify the final calculation: 3 / 1 = 3.

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