What is the projection of vector A = 3i + 4j onto vector B = 2i + 0j?

₹0.0

Question: What is the projection of vector A = 3i + 4j onto vector B = 2i + 0j?

Options:

Correct Answer: 6

Solution:

Projection of A onto B = (A · B / |B|^2)B. A · B = 6, |B|^2 = 4. Projection = (6/4)(2i) = 3i.

What is the projection of vector A = 3i + 4j onto vector B = 2i + 0j?

What is the projection of vector A = 3i + 4j onto vector B = 2i + 0j?

Step 1: Identify vector A and vector B. A = 3i + 4j and B = 2i + 0j.
Step 2: Calculate the dot product of A and B, denoted as A · B. This is done by multiplying the corresponding components: (3 * 2) + (4 * 0) = 6.
Step 3: Calculate the magnitude squared of vector B, denoted as |B|^2. This is done by squaring the components of B: (2^2) + (0^2) = 4.
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 into the formula: Projection = (6 / 4) * (2i + 0j).
Step 6: Simplify the expression: (6 / 4) = 1.5, so Projection = 1.5 * (2i) = 3i.

No concepts available.