How do you find the magnitude of YZ given Y(5,0) and Z(7,6)?
1 Answer
# bb(vec(YZ)) = ( (2), (6) ) \ \ # and# \ \ abs(bb(vec(YZ))) = 2sqrt(10) #
Explanation:
We have
So in vector notation we can write:
# bb(vec(OY)) = ( (5), (0) ) \ \ # and# \ \ bb(vec(OZ)) = ( (7), (6) ) #
We can calculate
Method 1:
Using the coordinates along, we can apply pythagoras theorem:
# YZ^2 = (7-5)^2 + (6-0)^2 #
# \ \ \ \ \ \ \ = 2^2 + 6^2 #
# \ \ \ \ \ \ \ = 4+36 #
# \ \ \ \ \ \ \ = 40 #
And so
Method 2:
Using vector notation we can calculate the vector
We have:
# bb(vec(YZ)) = bb(vec(OZ)) - bb(vec(OY)) #
# \ \ \ \ \ \ = ( (7), (6) ) - ( (5), (0) ) #
# \ \ \ \ \ \ = ( (7-5), (6-0) ) #
# \ \ \ \ \ \ = ( (2), (6) ) #
And so:
# abs(bb(vec(YZ))) = sqrt(2^2+6^2) #
# \ \ \ \ \ \ \ \ = 2sqrt(10) # , as before.