Given the displacement vector D = (2î − 6ĵ) m, find the displacement vector (in m) R so that D + R = −5Dĵ.

R = (-2î − 6ĵ + 10k^)m

Explanation:

We are given;

D = (2î − 6ĵ)

Now, we want to find R such that,

D + R = −5Dĵ

Plugging in (2î − 6ĵ) for D in the R equation gives;

(2î − 6ĵ) + R = -5(2î − 6ĵ)j

(2î − 6ĵ) + R = -10k + 0

This is because in vector multiplication, i × j = k and j × j = 0

Thus;

(2î − 6ĵ) + R = -10k

Making R the subject gives;

R = -2î − 6ĵ + 10k^

Thus, the displacement vector R is;

R = (-2î − 6ĵ + 10k^)m