Question

Show that the force vector →D=(2.0ˆi−4.0ˆj+ˆk)N is orthogonal to the force vector →G=(3.0ˆi+4.0ˆj+10.0ˆk)N.

a) →D and →G are not orthogonal
b) →D and →G are orthogonal
c) Cannot determine orthogonality without magnitudes
d) Orthogonality depends on the unit vectors used

Answer 1

The dot product between force vectors →D and →G equals zero, indicating that the vectors are orthogonal; hence, option b) →D and →G are orthogonal is correct.

Step-by-step explanation:

To show that the force vector →D = (2.0ˆi - 4.0ˆj + ˆk)N is orthogonal to the force vector →G = (3.0ˆi + 4.0ˆj + 10.0ˆk)N, we can use the dot product of the two vectors. If the dot product is zero, it indicates that the vectors are orthogonal.

The dot product →D · →G is calculated as:

(2.0)(3.0) + (-4.0)(4.0) + (1.0)(10.0) = 6.0 - 16.0 + 10.0 = 0 N

Since the dot product is zero, →D and →G are indeed orthogonal, which corresponds to option b).