Question

A position vector with magnitude 10 m points to the right and up. its x-component is 6.0 m. part a what is the value of its y-component?

Answer 1

The position vector can be transcribed as:

A = 6 i + y j                           

i points in the x-direction and j points in the y-direction.

The magnitude of the vector is its dot product with itself:

|A|2 = A·A

102  = (6 i + y j)•(6 i+ y j)            Note that i•j = 0, and  i•i  = j•j = 1 

100  = 36 + y2       

64    = y2

get the square root of 64 = 8

The vertical component of the vector is 8 cm.