Question

From the list below, select the vector that is not orthogonal (perpendicular) to:

a) Vector (1, 0, 0)
b) Vector (0, 1, 0)
c) Vector (0, 0, 1)
d) Vector (1, 1, 1)

Answer 1

d. Vector (1, 1, 1) is not orthogonal to vectors (1, 0, 0), (0, 1, 0), or (0, 0, 1) because its dot product with each of them is not zero. The dot products give values of 1, indicating the vectors are not perpendicular.

Step-by-step explanation:

The subject of this question is determining which of the given vectors is not orthogonal (not perpendicular) to vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1). Vectors are orthogonal if their dot product is zero. The dot product of two vectors A = (a1, a2, a3) and B = (b1, b2, b3) is given by A · B = a1*b1 + a2*b2 + a3*b3.

For vectors (1, 0, 0), (0, 1, 0), and (0, 0, 1), their dot products with the vector (1, 1, 1) would be:

• (1, 0, 0) · (1, 1, 1) = 1*1 + 0*1 + 0*1 = 1
• (0, 1, 0) · (1, 1, 1) = 0*1 + 1*1 + 0*1 = 1
• (0, 0, 1) · (1, 1, 1) = 0*1 + 0*1 + 1*1 = 1

Since the dot products are not zero, vector (1, 1, 1) is not orthogonal to any of the vectors (1, 0, 0), (0, 1, 0), or (0, 0, 1). Therefore, the vector that is not orthogonal to the given vectors a, b, and c is vector d, which is (1, 1, 1).