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=√(105)`

`\mid\mid \vec A-\vec B \mid \mid=√(149)`

Step-by-step 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=√(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=√((-2)^2+10^2+(-1)^2)=√(4+100+1)`

`\mathbf{\mid\mid \vec A+\vec B \mid \mid=√(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=√(8^2+(-6)^2+7^2)=√(64+36+49)`

`\mathbf{\mid\mid \vec A-\vec B \mid \mid=√(149)}`