Question

Determine 3a, a + b, a – b, |a + b|, |a − b| for the given vectors:

A a = 2i + 4j, b = -i + 4j
B a = (1, 1, 1), b = (2, 3, -1)
C a = (7, 10), b = (1, 2, 3)

Answer 1

To determine 3a, a + b, a - b, |a + b|, and |a - b| for the given vectors A a = 2i + 4j, b = -i + 4j, perform vector operations.

Step-by-step explanation:

To determine 3a, a + b, a - b, |a + b|, and |a - b| for the given vectors, we need to perform vector operations.

For vectors A a = 2i + 4j, b = -i + 4j, we have:

3a = 3(2i + 4j) = 6i + 12j

a + b = (2i + 4j) + (-i + 4j) = i + 8j

a - b = (2i + 4j) - (-i + 4j) = 3i

|a + b| = |i + 8j| = sqrt(1^2 + 8^2) = sqrt(65)

|a - b| = |3i| = 3