Question

If A=3i +2j+3k ,find the magnitude of A+B and A-B​

Answer 1

Since vector B was not specified, I'll assume one at random. You can later answer your own question.

Answer:

$\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}$

$\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}$

Explanation:

Given:

$\vec A=3\hat i +2\hat j+3\hat k$

And (assumed):

$\vec B=-5\hat i +8\hat j-4\hat k$

Find the magnitude of

$\vec A+\vec B$

$\vec A-\vec B$

Given a vector

$\vec P=x\hat i +y\hat j+z\hat k$

The magnitude of the vector is:

$\mid\mid \vec P\mid \mid=\sqrt{x^2+y^2+z^2}$

• First part:

$\vec A+\vec B =3\hat i +2\hat j+3\hat k-5\hat i +8\hat j-4\hat k$

$\vec A+\vec B =-2\hat i +10\hat j-\hat k$

The magnitude of the sum is:

$\mid\mid \vec A+\vec B \mid \mid=\sqrt{(-2)^2+10^2+(-1)^2}=\sqrt{4+100+1}$

$\mathbf{\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}}$

• Second part:

$\vec A-\vec B =3\hat i +2\hat j+3\hat k-(-5\hat i +8\hat j-4\hat k)$

$\vec A-\vec B =3\hat i +2\hat j+3\hat k+5\hat i -8\hat j+4\hat k$

$\vec A-\vec B =8\hat i -6\hat j+7\hat k$

The magnitude of the difference is:

$\mid\mid \vec A-\vec B \mid \mid=\sqrt{8^2+(-6)^2+7^2}=\sqrt{64+36+49}$

$\mathbf{\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}}$