How do you find the component form and magnitude of the vector v given initial point (1,11) and terminal point (9,3)?

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Answer 1 · 2017-08-18T23:08:06

# bb(ul v) = ( (8), (-8) ) = << 8, -8 >> = 8bb(ul hat i) - 8bb(ul hat j)#

# || bb(ul v) || = 8sqrt(2) #

Denote the given coordinates by:

# O= (0,0) #
# A = (1,11) #
# B = (9,3) #

Then the vector #bb(ul v)# is given by:

# bb(ul v) = bb(vec(OB)) - bb(vec(OA)) #
# \ \ \ = ( (9), (3) ) - ( (1), (11) )#
# \ \ \ = ( (8), (-8) )#

Alternatively, depending upon the desired notation we can also write:

# bb(ul v) = << 8, -8 >> = 8bb(ul hat i) - 8bb(ul hat j)#

And we can calculate the magnitude, using the metric norm:

# || bb(ul v) || = sqrt((8)^2 + (-8)^2 ) #
# " " = sqrt(64+64) #
# " " = sqrt(128) #
# " " = 8sqrt(2) #