Question

For the vectors a = 16i - 8j, b=-2i+4j-k, and c = 5i - j + 3k, construct the vector m = c + 5b - a/8,

What are the components of vector m?

a) m = (-7i - 22j - 2k)
b) m = (7i + 22j + 2k)
c) m = (-7i + 22j - 2k)
d) m = (7i - 22j + 2k)

Answer 1

To construct the vector m = c + 5b - a/8, add the corresponding components of c, 5b, and -a/8. The components of vector m are (-12i + 20j - 5k + j/8).

Step-by-step explanation:

To construct the vector m = c + 5b - a/8, we need to add the corresponding components of vectors c, 5b, and -a/8. Let's break down each step:

1. Add the components of c:

m = 5i - j + 3k

2. Multiply the components of vector b by 5:

m = 5*(-2i + 4j - k)

= -10i + 20j - 5k

3. Divide the components of vector a by 8 and subtract them from m:

m = -10i + 20j - 5k - (16i - 8j)/8

= -10i + 20j - 5k - 2i + j/8

= -12i + 20j - 5k + j/8

Therefore, the components of vector m are:

m = (-12i + 20j - 5k + j/8)