Question

Find the sum of the vectors $\vec{a}=\hat i -2\hat j+\hat k, \vec{b}=-2\hat i +4\hat j+5\hat k \ and\ \vec{c}=\hat i -6\hat j-7 \hat k.$

Answer 1

To find the sum of the vectors

$\vec{a}=\hat i -2\hat j+\hat k, \vec{b}=-2\hat i +4\hat j+5\hat k \ \\and\ \vec{c}=\hat i -6\hat j-7 \hat k.$

add components of i with i,j with j and k with k

Let the resultant vector is p

$\vec{p}=\vec{a}+\vec{b}+\vec{c}=\\\\\hat i -2\hat j+\hat k+(-2\hat i +4\hat j+5\hat k)+\hat i -6\hat j-7 \hat k$

$\vec{p}=\hat i(1-2+1)+\hat j(-2+4-6)+\hat k(1+5-7)\\\\=\hat i(0)+\hat j(-4)+\hat k(-1)\\\\\vec{p}=-4\hat j-\hat k$