Question

If A=I+2j+k, B=2i+3k and C=2i+4k, then magnitude of vectorA+B-C is

Answer 1

Given:

$\vec{A}= \hat{i}+2 \hat{j}+ \hat{k}$

$\vec{B}= 2 \hat{i}+ 3\hat{k}$

$\vec{C}= 2 \hat{i}+ 4\hat{k}$

To find:

The magnitude of A+B-C

Solution:

Now, required vector is :

$\vec{A} + \vec{B} - \vec{C}$

$= \hat{i} + 2 \hat{j}$

Now, required magnitude is :

$| \vec{A} + \vec{B} - \vec{C} | = \sqrt{ {1}^{2} + {2}^{2} }$

$\implies | \vec{A} + \vec{B} - \vec{C} | = \sqrt{1 + 4 }$

$\implies | \vec{A} + \vec{B} - \vec{C} | = \sqrt{5 }$

So, required magnitude is √5.