Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).

Find the scalar projection of vector A = (3, 4) onto vector B = (1, 0).

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.

Scalar Projection – The scalar projection of vector A onto vector B is the length of the orthogonal projection of A in the direction of B, calculated using the dot product and the magnitude of B.
Dot Product – The dot product of two vectors is a scalar value that represents the product of their magnitudes and the cosine of the angle between them.
Magnitude of a Vector – The magnitude of a vector is the length of the vector, calculated as the square root of the sum of the squares of its components.