Question

If a vector equals to 3i^ + 2j^ and b vector is equals to 2i^+ 3 j^ - k^and find a unit vector along a vector minus b vector​

Answer 1

We have been given 2 vectors .

$\vec a = 3 \hat i + 2 \hat j$

$\vec b = 2 \hat i + 3 \hat j - \hat k$

We have to find a unit vector along the difference of the 2 vectors .

Let the difference be $\vec c$

$\vec c = \vec a - \vec b$

$= > \vec c = (3 - 2) \hat i + (2 - 3) \hat j -( - \hat k)$

$= > \vec c = \hat i - \hat j + \hat k$

Now unit vector can be obtained by dividing the actual vector by its magnitude :

$\therefore \: \hat c = \dfrac{ \vec c}{ | \vec c| }$

$= > \: \hat c = \dfrac{ \hat i - \hat j + \hat k}{ \sqrt{ {1}^{2} + {( - 1)}^{2} + {1}^{2} } }$

$= > \: \hat c = \dfrac{ \hat i - \hat j + \hat k}{ \sqrt{ 3} }$

So final answer is :

$\boxed{ \red{ \huge{ \bold{\: \hat c = \dfrac{ \hat i - \hat j + \hat k}{ \sqrt{ 3} } }}}}$

Answer 2

• Vectors are the physical quantities that has both direction and magnitude.

• Unit vector is the vector that has the magnitude as unity or 1. It is represent with a symbol ^ on the vector and said as 'Cap'.

There are also some kinds of vector such as :

◾Collinear vector

◾Coplanar vector

◾Negative vectors

◾Equal vectors

Refer to the attachment for the solution.

$Ans: \: (\frac{i - j + k}{ \sqrt{3} } )$