Q. If vectors A=i+2j+4k and B=5i represent the two sides of a triangle, then the third side of the triangle can have length equal to:
a) 6
b)$\sqrt{56}$
c)both (a) and (b)
d)none of the above
Following directly into the answer: A+B=6i+2j+4k then the magnitude of A+B (which is the line that makes will be $\sqrt{56}$ and hence option 'b'. But my text marks the answer as 'c'.
But how can this happen if both A and B are specific vectors and has only one magnitude and a single direction can have two different resultants? Am I wrong somewhere, or is it my textbook?
You get two answers because you can form two essentially different triangles: one triangle by matching the tip of one vector to the tail of the second and another triangle by matching the tails of the two vectors.