What is the value of its y-component?

Question

A position vector with magnitude 10m points to the right & up.  Its x-component is 6.0m.  What is the value of its y-component?

Answer 1

Hi Kayla,

 

The position vector can be written 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                           The vertical component of the vector is  8 cm