Question

Let vectors A = (2, −1, 1), B = (3, 0, 5), and C = (1,4,-2), where (x, y, z) are the components of the vectors along the x, y, and z axes, respectively; and let A, B and C be the magnitudes of A, B, and C, respectively.

Calculate 2A +3B+C.
Express the components numerically to two significant figures separated by commas.

Answer 1

The sum of the vectors 2A, 3B, and C is found by adding their corresponding components, resulting in the vector (14, 2, 15).

Step-by-step explanation:

To calculate the sum of the vectors 2A, 3B, and C, we need to add the vectors by their corresponding components along the x, y, and z axes. This is known as vector addition. Multiplying vector A by 2 scales its components by 2, multiplying vector B by 3 scales its components by 3, and vector C remains unchanged.

The components of vector A are (2, -1, 1), of vector B are (3, 0, 5), and of vector C are (1, 4, -2).

2A has components (4, -2, 2), 3B has components (9, 0, 15), and C is (1, 4, -2).

Now, add the components of these vectors:

• x-components: 4 + 9 + 1 = 14
• y-components: -2 + 0 + 4 = 2
• z-components: 2 + 15 - 2 = 15

Therefore, 2A + 3B + C = (14, 2, 15).