Finding a column vector.

Question

Question: Given that column vector AB is $AB=<a,3>$ and column vector AC is $AC=<-5,0>$, Find the value of a if the vectors AB and AC are two sides of a rhombus.

I thought of solving it using the magnitude of the two vectors AB and AC but I don’t know how to relate the two of them.

Answer 1

• Vectors $AB$ and $AC$ start from the same point ($A$)
• Rhombi have equal side lengths.
• Hence $\|{AB}\| = \|{AC}\|$
• Find the magnitude of each, set them equal to each other, and solve for $a$.