Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
0 votes

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} $

Can you answer this question?

1 Answer

0 votes
  • 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.
$(1-2+1)\hat i+(-2+4-6)\hat j+(1+5-7)\hat k=0\hat i-4\hat j-\hat k$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\;=0\hat i-4\hat j-\hat k$
$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\;\;=-4\hat j-\hat k$
answered May 17, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App