Question

The two vectors a=⟨−1,2,−4⟩ and b=(2,−4,−8), are not parallel but are orthogonal. Select one:

A.True
B.False

Answer 1

The two vectors are neither orthogonal nor parallel, as their dot product is not zero and their corresponding components do not have a constant ratio. Therefore, the statement is False.

Step-by-step explanation:

To determine if two vectors are orthogonal or parallel, we need to check their scalar (dot) product and compare their directions. For vectors a=\langle -1,2,-4 \rangle and b=(2,-4,-8), we calculate the dot product:

a \cdot b = (-1)(2) + (2)(-4) + (-4)(-8) = -2 - 8 + 32 = 22.

Because the dot product is not zero (22 \\eq 0), the vectors are not orthogonal. And since the ratios of the corresponding components of a and b are not constant (i.e., -1/2 \\eq 2/-4 \\eq -4/-8), the vectors are not parallel either. Hence, the statement "The two vectors a=\langle -1,2,-4 \rangle and b=(2,-4,-8), are not parallel but are orthogonal." is False.