Question

If A = [3, 0, 1], find a vector B such that comp(B, A) = 0.

a) B = [1, 0, 3]
b) B = [0, 1, -3]
c) B = [-3, 0, 1]
d) B = [0, 3, 1]

Answer 1

To find a vector B such that comp(B, A) = 0, we need to find a vector B that is orthogonal (perpendicular) to vector A.

Step-by-step explanation:

To find a vector B such that comp(B, A) = 0, we need to find a vector B that is orthogonal (perpendicular) to vector A. In other words, the dot product of vectors A and B should be zero. The dot product of two vectors can be found using the formula: A dot B = |A||B|cos(theta), where |A| and |B| are the magnitudes of vectors A and B, and theta is the angle between them. In this case, vector A = [3, 0, 1]. To find vector B, we can set up the equation: 3B1 + 0B2 + B3 = 0.

Since the dot product of the two vectors should be zero, we know that the y-component of vector B (B2) can be any value. Let's assume B2 = 1. Substituting the values into the equation, we get: 3B1 + 0 + B3 = 0. Simplifying, we have: 3B1 + B3 = 0. We can choose any numerical value for B1 and B3 as long as they satisfy this equation. For example, let's choose B1 = 1 and B3 = -3. Therefore, vector B = [1, 1, -3] is a vector that is orthogonal to vector A and has a dot product of zero.

In conclusion, vector B = [1, 1, -3] is a vector such that comp(B, A) = 0.