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Q1) Referred to a fixed origin, the line L1 has the equation r=12i+15j+k+s(2i+j+k) and the line L2 has the equation r=i+j-2k+t(3i-k)

a) Show that the lines L1 and L2 intersect and find the position vector of A, their point of intersection

b) Find, to the nearest degree, the acute angle between the lines L1 and L2

The point B with position vector 16i+7j+3k lies on the line L1. The point C with position vector 22i+j-9K and the point D both lie on the line L2.

c)Given that BD is perpendicular to AC, find the position vector of D

d)Hence, or otherwise, prove that ?ABC is isosceles

Thank you for the help in advance....I REALLY APPRECIATE IT!!
2. 1) Equate the two lines to form 3 equations in 2 unknowns, s and t. Solve one pair and you must verify the third equation.
2) Use formula cos(theta) = (a.b)/(|a|*|b|), just remember to use the direction vectors of each line.
3) Perpendicular means the dot product is equal to zero...
3. (Original post by vc94)
1) Equate the two lines to form 3 equations in 2 unknowns, s and t. Solve one pair and you must verify the third equation.
2) Use formula cos(theta) = (a.b)/(|a|*|b|), just remember to use the direction vectors of each line.
3) Perpendicular means the dot product is equal to zero...
Thanks for the help....I seriously appreciate it

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