Question

Find the magnitude of the vector with (8,-6) and write the vector as the sum of unit vectors.

Answer 1

The magnitude of a vector is simply the Pythagorean Theorem!

`√(a^2+b^2) = magnitude`
a=8, b=-6


`√(8^2+(-6)^2) = magnitude`
magnitude = 10


Unit vector: (8/10, -6/10).
Divide by 10!(magnitude)

Answer 2

The magnitude is 10 units.

Explanation:

we have to find the magnitude of vector and also vector as the sum of unit vectors.

The magnitude of a vector is simply the Pythagorean Theorem

`√(a^2+b^2) = ||(a,b)||`

a=8, b=-6

`√(8^2+(-6)^2) = ||(8,-6)||`

`magnitude = √(64+36)=√(100)=10 units`

The unit vector is

`<8,-6>=<(8)/(10),(-6)/(10)>`

And in unit vector form, we have:

`<8,-6>=8\hat{i}-6\hat{j}`