What is the length PC? How did you solve this?

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1 Answer
Apr 6, 2018

Answer:

See below.

Explanation:

Calling

#vec v_1, vec v_2, vec v_3# the unit vectors with the direction of #A-P, B-P# and #C-P# we have

#A = P + a vec v_1#
#B = P + b vec v_2#
#C = P + c vec v_3#

Here

#a = 10#
#b = 6#

then

#B-A = b vec v_2-a vec v_1#
#C-B = c vec v_3 - b vec v_2#

but #B-A# and #C-B# are perpendicular then

# << B-A, C-B >> = << b vec v_2-a vec v_1, c vec v_3 - b vec v_2 >> = 0#

#b c << vec v_2, vec v_3 >> - b^2 norm(vec v_2)^2-ac << vec v_1, vec v_3 >>+a b << vec v_1, vec v_2 >> =0#

and then

#c = (b^2-ab << vec v_1, vec v_2>>)/(b << vec v_2, vec v_3 >> - a << vec v_1, vec v_3>>) = 33#

with

# << vec v_1, vec v_2 >> =-1/2#
# << vec v_2, vec v_3 >> =-1/2#
#<< vec v_1, vec v_3 >> = -1/2 #

NOTE

#<< cdot, cdot >># represents the scalar product of two vectors.
#norm(cdot)# represents the norm operation.