Find a vector of magnitude 5 units, and parallel to the resultant of the vectors vector(a) = 2i + 3j - k and vector(b) = i - 2j - k.

Question

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors \(\vec{a}=2\hat{i}+3\hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}-2\hat{j}-\hat{k}.\)

Answer 1

Given, two vectors are \(\vec{a}=2\hat{i}+3\hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}-2\hat{j}+\hat{k}\)

If \(\vec{c}\) is the resultant vector of \(\vec{a}\) and \(\vec{b}\) then

Now, a vector having magnitude 5 and parallel to \(\vec{c}\) is given by

It is required vector.

[Note: A vector having magnitude I and parallel to \(\vec{a}\) is given l. \(\frac{\vec{a}}{|\vec{a}|}.]\)