Calculus/Vectors 3d

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Expert: - 2/9/2009


Question
I dont understand this topic. Please help me, i need the whole solutions. The points A,B,C and D have position vectors a,b,c,d respectively,given by a=i-j+2k,b=3i+7j-k,c=4i+15j+10k, & d=2i+ 18j +2k.a) find,in vector form,an equation for the line l which passes through A & B.b) find a vector equation of the plane ¥ which passes through D & is perpendicular to line l. Find also the position vector of the point E in which l & ¥ intersect. Deduce the position vector of the image of the point B under a reflection in the plane ¥.c) find the acute angle that the CD makes with the plane ¥. Thanks

Answer
A =  i -  j  +  2k
B = 3i + 7j  -   k
C = 4i + 15j + 10k
D = 2i + 18j +  2k

a) To pass through A and B, take (B-A)t + A.

b) If a line L is ax+by+cz = K, the perpendicular vector is
(a,b,c)t.  To pass through D, it uses (a,b,c)t + (2,18,2).

c) Take D - C.  Once this vector is found, find the angle Θ that
this line makes with the normal vector in degrees.  The angle that
that this line makes with the plane would be 90° - Θ.  To find the
angle, note that A x B =  ab sin(Θ) N where N is the perpendiuclar
vector to the plane with A and B defining it.

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