Linear Algebra, Lines & Planes in 3-space problems? Simple questions Plz Help in detail?

Question

Plz guide me in the following questions, step by step & plz write all important formulas, since my Linear Algebra is not good:

5b-Determine whether the planes are parallel
x-4y-3z-2=0 and 3x-12y-9z-7=0

7b-Determine whether the planes are perpendicular
x-2y+3z=4, -2x+5y+4x=-1

10a-Find parametric equation for the line passing through the given points
(5,-2.4), (7, 2,-4). Answer: x=5+t, y=-2+2t, z=4-4t

11a-Find Parametric equations for the line of intersection of the given points
7x-2y+3z=-2 and -3x+y+2z+5=0 Ans.: x=-12-7t, y=-41-23t, z=t

14a-Determine whether the planes are perpendicular
(-2,1,4).(x-1,y,z+3)=0;(1,-2,1).(x+3,y-5,z)=0

16-Line
x=0, y=t, z=t (-Infinity < t < +Infinity)

a-lies in the plane 6x+4y-4z=0
b-is parallel to and below the plane 5x-3y+3z=1
c-is parallel to and above the plane 6x+2y-2y=3

17-Find equation for the plane through (-2,1,7) that is perpendicular to the line x-4=2t, y+2=t, z=-5t. Ans.: 2x+3y-5z+36=0

22-Find the point of intersection of the line
x-9=-5t, y+1=-t, z-3=t (-Infinity and the plane 2x-3y+4z+7=0
Ans.: (-173/3,-43/3,49/3)

23-Find equation for the plane that contains the line x= -1+3t, y=5+2t, z=2-t and is perpendicular to the plane 2x-4y+2z=9
Ans.: y+2z-9=0

25-Show that the points (-1,-2,-3),(-2,0,1)(-4,-1,-1) and (2,0,1) lie in the same plane.


and if u could provide me ur E-mail address to have future contact in order to ask questions of MATHEMATICS. Thank u

Answer 1

5b. Look at the normals. You have <1,-4,-3> for the first, and <3,-12,-9> for the second. Since the second is a scalar multiple of the first, the normals are parallel, so the planes are, too.

7b. Again, look at the normals. They are <1.-2,3> and <-2,5,4>. Their dot (inner) product is 1*(-2) + (-2)*5 + 3*4 = 0. Thus, the normals are orthogonal, so the planes are perpendicular.

You ask too much.

Answer 2

square of any numbers means multiplying the number by itself square of x means x × x = x² similarly square of 7 = 7 × 7 = 49 or it is written as 7² = 49 -----