1. l:r = 2i – 3j + 5k + t ( i – j – k ), point P(0,-1,7) lies on the line l. The angle between OP and the line l.
2. Point A(1,4,-3), B(5,6,-1) and C(-3,1,2). The plane π contains points A, B and C. Find the angle between the line OC and π.
Please help me to find a correct and show me the way to do it
I just got it wrong so please help.
i- j- k is, of course, a vector in the direction of line l. The vector -j+ 7k is in the direction of the line OP. And, of course, where is the angle between the two vectors.
Again, a vector in the direction of OC is -3i+ j+ 2k. The vector AC is (-3-1)i+ (1-4)j+(2-(-3))k= -4i- 3j+ 5k and the vector AB is the (5- 1)i+ (6- 4)j+ (-1-(-3))k= 4i+ 2j+ 3k. The normal vector to the plane is the cross product of those two. After you find the angle between OC and the normal to the plane, the angle between OC and the plane is its complement.2. Point A(1,4,-3), B(5,6,-1) and C(-3,1,2). The plane π contains points A, B and C. Find the angle between the line OC and π.
Please help me to find a correct and show me the way to do it
I just got it wrong so please help.