Given the planes P1 : x + 4y − z = 10, P2 : 3x − y + 2z = 4, and the point A (−2, 1, 0).

(a) Determine an equation for the plane that contains A and is parallel to P1.
(b) Determine whether A lies on P2. If it doesn’t, find the distance from A to P2.

a) x+4y-z=2

b)   -7/

Step-by-step explanation:

a)

Equation of a plane containing point A is given by;

[x-(-2)]+[y-1]+[z-0]=0 ----(1)

If this plane is parallel to the plane P1 whose normal vector is {1.4.-1] - then this will also be normal to plane (1)

so,

(1)[x-(-2)]+(4)[y-1]+(-1)[z-0]=0

==> x+2+4y-4-z=0

==> x+4y-z=2

will be the plane parallel to P1

b) If A lies on P2 then it should satisfy the equation of P2

Putting x= -2, y=1 and z= 0

==> 3(-2)-(1)+2(0)=4

==>-6-1+0=4

==> 5=4

which is not true i-e equation is not satisfied ! So the point lies out of plane. Lets find distance from P2 of point A

We know distance of point (x1,y1,z1) from a plane Ax+By+CZ+D=0 is

d= Ax1+By1+Cz1+D /

So distance of point A from P2 is;

d= 3×(-2)-1(1)+2(0)/

==> d= -7/

the size of the resulting matrix is 1-by-3.

step-by-step explanation:

the size of the two matrices given are as follows:

no .of rows of matrix 1 = 1

no .of columns of matrix 1 = 3

no .of rows of matrix 1 = 3

no .of columns of matrix 1 = 3

to find the size of the resulting matrix without actually solving the multiplication of the matrix, this is what you do:

if resulting matrix = matrix 1 * matrix 2

no. of rows of the resulting matrix = number of rows of matrix 1

no. of columns of resulting matrix = number of columns of matrix 2

note: the order of the matrices matter!

it could 14.28 but if its not that one then it has to be the 17 one. hope this ! : )

step-by-step explanation: