1.) Show that
det ( 1+x 2 3 4
1 2+x 3 4
1 2 3+x 4
1 2 3 4+x)
= x^3 (x+10)
It should be easy but I dont know why I cannot get the answer
Please help!
2.) Consider the triangle ABC formed by the points A(3,2,1), B(4,4,2) and C(6,1,0). Find the coordinates of point D on BC such that AD is perpendicular to BC. (ans: 1/17 (80 50 22)T)
THANKS A LOT!!
Any point on BC has coordinates x= 4+ (6- 4)t= 4+ 2t, y= 4+ (1- 4)t= 4- 3t, and z= 2+ (0- 2)t= 2- 2t.2.) Consider the triangle ABC formed by the points A(3,2,1), B(4,4,2) and C(6,1,0). Find the coordinates of point D on BC such that AD is perpendicular to BC. (ans: 1/17 (80 50 22)T)
Let D have coordinates (x, y, z). Then the vector AD is (x- 3)i+ (y- 2)j+ (z- 1)k and BC is 2i- 3j- 2k. The dot product of those two vectors is 0. Replacing x, y, and z with there expression in t gives a single equation for t.