Mathematics

Mathematics

Problem

6. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a⃗=2i^+3j^−k^\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k} and b⃗=i^−2j^+k^\vec{b}=\hat{i}-2 \hat{j}+\hat{k}.
Intuitive explanation

The key is to find the resultant vector first, then scale it to have magnitude 5. Two vectors are parallel when one is a scalar multiple of the other, so you'll add a⃗\vec{a} and b⃗\vec{b} to get their resultant, calculate its magnitude, then multiply by the scaling factor that makes your final answer have magnitude exactly 5.

Intuitive explanation

The key is to find the resultant vector first, then scale it to have magnitude 5. Two vectors are parallel when one is a scalar multiple of the other, so you'll add a⃗\vec{a} and b⃗\vec{b} to get their resultant, calculate its magnitude, then multiply by the scaling factor that makes your final answer have magnitude exactly 5.

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