What is the scalar projection of vector H = 6i + 8j onto vector I = 3i + 4j?

₹0.0

Question: What is the scalar projection of vector H = 6i + 8j onto vector I = 3i + 4j?

Options:

Correct Answer: 10

Solution:

Scalar projection = (H · I) / |I| = (6*3 + 8*4) / √(3^2 + 4^2) = (18 + 32) / 5 = 50 / 5 = 10.

What is the scalar projection of vector H = 6i + 8j onto vector I = 3i + 4j?

What is the scalar projection of vector H = 6i + 8j onto vector I = 3i + 4j?

Step 1: Identify the vectors. H = 6i + 8j and I = 3i + 4j.
Step 2: Calculate the dot product of H and I. This is done by multiplying the corresponding components: (6 * 3) + (8 * 4).
Step 3: Perform the multiplication: 6 * 3 = 18 and 8 * 4 = 32.
Step 4: Add the results of the multiplication: 18 + 32 = 50.
Step 5: Calculate the magnitude (length) of vector I. This is done using the formula |I| = √(3^2 + 4^2).
Step 6: Calculate 3^2 = 9 and 4^2 = 16.
Step 7: Add the squares: 9 + 16 = 25.
Step 8: Take the square root of 25: √25 = 5.
Step 9: Now, use the formula for scalar projection: Scalar projection = (H · I) / |I|.
Step 10: Substitute the values: Scalar projection = 50 / 5.
Step 11: Perform the division: 50 / 5 = 10.

No concepts available.