How do you find the magnitude of <5,6> and write it as a sum of the unit vectors?

1 Answer
Nathan L.
Aug 5, 2017

"magnitude" = 7.810

< 5,6 > = 5hati + 6hatj

Explanation:

We'll call the given vector vecA with components A_x = 5 and A_y = 6.

The magnitude of a vector is given by

|vecA| = sqrt((A_x)^2 + (A_y)^2) = sqrt(5^2 + 6^2) = color(blue)(ulbar(|stackrel(" ")(" "7.810" ")|)

" "

Vectors in the notation < x,y > can also be represented by unit vectors, with the unit vector hati for the x-component and hatj for the y-component:

< 5,6 > = color(blue)(ulbar(|stackrel(" ")(" "5hati + 6hatj" ")|)

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