Question

PartA Can you resolve a 3-D vector along two different directions (random), which are not at 90 to each other? @ Yes, but not uniguely O No Yes, uniquely Yes only when they are 909 to each other

Answer 1

A 3-D vector can be defined as a line segment extending in three co-ordinate planes which are represented as x, y and z plane. To resolve a vector, say r along three planes, let there are two different resolutions as follows: gâ+ Bb +7 rea'a+B'5+y'c In the above resolutions, a.ß.7.a.ß.7 are scalars. Since both the above vectors are same so, the above two equations should be equal, that is, aã+B7+yc = a'a+B'5+y't (a-a'a+(B-B")+(Y-Y')=0 As the vectors a,b and care non-coplanar so their coefficients must be zero, because a linear combination of three non-planar vectors cannot be non-zero. Therefore, ara B=B v=y' This implies that the resolution of a 3-D vector along two different directions is unique. Thus, the second option is the correct choice.