Answer: The answer is either letter A or letter D
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Hint 1: Find the direction cosines of AB and BC. Then take their dot product. This will give the cosine of the angle between AB and BC.
Hint 2: The Direction Cosines of PQ, P(x1,y1,z1) and Q(x2,y2,z2), are (±x2−x1(x2−x1)2+(y2−y1)2+(z2−z1)2√,±y2−y1(x2−x1)2+(y2−y1)2+(z2−z1)2√,±z2−z1(x2−x1)2+(y2−y1)2+(z2−z1)2√)
Edit: The Dot Product works iff the lines intersect.
B is the intersect point , doesn't matter if it's in 2D or 3D – Ali Apr 28 '18 at 5:52
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Lines in dimension three do not have to intersect. We find their direction vectors to see if they are parallel.
Note that
AB→=<x2−x1,y2−y1,z2−z1>
and
BC→=<x3−x2,y3−y2,z3−z2>
These vectors are the direction vectors are your lines.
The dot product
AB→.BC→
along with the norms of these vectors determine the angle between the lines if they intersect at all.
cosθ=AB→.BC→||AB||.||BC||
Step-by-step explanation: This is for the picture
Center: (0, 0)
Width: 10
Angle: 0 rad
Height: 6.8
Opacity: 1
