Answer:
Explanation:
For two vectors to be orthogonal (perpendicular) the product of both vectors must be zero. Given the vectors D=(2.0i-4.0j+k)N and G=(3.0i+4.0j+10k)N, to show that they are orthogonal, we will take their dot product as shown;
D.G = (2.0i-4.0j+k).(3.0i+4.0j+10k)
Note that i.1 = j.j = k.k = 1 and dot product of different component is zero.
D.G = 2.0(3.0) (i.i) + (-4.0)(4.0)j.j + 1(10)k.k
D.G = 6.0(1) -(16)(1)+10(1)
D.G = 6-16+10
D.G = -10+10
D.G = 0
Since the dot product of the two vectors is zero, this shows that force vector D is orthogonal to force vector G.
