Browse Questions

# Find the sum of the vectors $\overrightarrow a=\hat i − 2\hat j + \hat k, \overrightarrow b=−2\hat i + 4\hat j + 5\hat k$ and $\overrightarrow c = \hat i − 6\hat j – 7\hat k$ .

$\begin{array}{1 1}(A) -4\hat j - \hat k. \\ (B) 4\hat j - \hat k. \\ (C) -4\hat i - \hat k. \\ (D) 4\hat i - \hat k.\end{array}$

Toolbox:
• Sum of the vectors : Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ can be added by adding their scalar components.
Step 1:
Let $\overrightarrow{a}=\hat i-2\hat j+\hat k$,$\overrightarrow{b}=-2\hat i+4\hat j+5\hat k$ and $\overrightarrow{c}=\hat i-6\hat j-7\hat k$
We are asked to find the sum of the vectors $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$
Sum of the vectors $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=(\hat i-2\hat j+\hat k)+(-2\hat i+4\hat j+5\hat k)+(\hat i-6\hat j-7\hat k)$
Step 2:
Now adding the scalar componens of $\hat i,\hat j$ and $\hat k$ respectively.
$(1-2+1)\hat i+(-2+4-6)\hat j+(1+5-7)\hat k=0\hat i-4\hat j-\hat k$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\;=0\hat i-4\hat j-\hat k$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\;=-4\hat j-\hat k$