Can you help me solve this?
a) Let u=(2, 3, -1) and w = (3, -1, p). Given that that u is perpendicular to w, find the value of p.
b) let v=(1, q, 5). Given that |v|= √42, find the possible values of q.
Thank you so much!
a) Let u=(2, 3, -1) and w = (3, -1, p). Given that that u is perpendicular to w, find the value of p.
b) let v=(1, q, 5). Given that |v|= √42, find the possible values of q.
Thank you so much!
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Here's some notes on dot products:
http://www.sparknotes.com/physics/vector…
a) If u and w are perpendicular, then u.w = 0.
u.w = 2.3+3.(-1)+(-1).p = 6-3-p = 3-p
For this to equal 0, p = 3.
b) |v|= √42 means that the square root of the dot product of v with itself = 42.
v.v = 1.1+q.q+5.5 = 1+q^2+25 = 26+q^2
For this to = 42, q^2 = 42-26 = 16 so q=4.
However, since the value of q is squared, a solution of q=-4 would also fit.
http://www.sparknotes.com/physics/vector…
a) If u and w are perpendicular, then u.w = 0.
u.w = 2.3+3.(-1)+(-1).p = 6-3-p = 3-p
For this to equal 0, p = 3.
b) |v|= √42 means that the square root of the dot product of v with itself = 42.
v.v = 1.1+q.q+5.5 = 1+q^2+25 = 26+q^2
For this to = 42, q^2 = 42-26 = 16 so q=4.
However, since the value of q is squared, a solution of q=-4 would also fit.