Ask Questions, Get Answers

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

If \( \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k\), then find a vector \( \overrightarrow c\) such that \( \overrightarrow a \) x \( \overrightarrow c = \overrightarrow b\: and \: \overrightarrow a.\overrightarrow c = 3 \)

Can you answer this question?

1 Answer

0 votes
  • $\hat i.\hat i=1$
  • $\hat j.\hat j=1$
  • $\hat k.\hat k=1$
Step 1:
$\overrightarrow a=\hat i+\hat j+\hat k$
$\overrightarrow b=\hat j-\hat k$
Given : $\overrightarrow a\times \overrightarrow c=\overrightarrow b$
$\overrightarrow a.\overrightarrow c=3$
Let $\overrightarrow c=x\hat i+y\hat j+z\hat k$
$\overrightarrow a\times \overrightarrow c=\overrightarrow b$
$\begin{vmatrix}\hat i&\hat j&\hat k\\1 & 1 & 1\\x& y&z\end{vmatrix}=\hat j-\hat k$
(i.e)$(z-y)\hat i-(z-x)\hat j+(y-x)\hat k=\hat j-\hat k$
Step 2:
Now equating the coefficients we get,
$\therefore z=x-1$
Step 3:
$\overrightarrow a.\overrightarrow c=3$
$\hat i+\hat j+\hat k.(x\hat i+y\hat j+z\hat k)=3$
$\therefore z=x-1,y=x-1$
$\overrightarrow c=\large\frac{5}{3}$$\hat i+\large\frac{2}{3}$$\hat j+\large\frac{5}{3}$$\hat k$
Hence the required vector $\overrightarrow c=\large\frac{5}{3}$$\hat i+\large\frac{2}{3}$$\hat j+\large\frac{5}{3}$$\hat k$
answered Oct 3, 2013 by sreemathi.v

Related questions

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