Gfind the equation for the plane containing the points (0, 0, 1), (1, 2, 3), (2, 4, 5), and (4, 8, 11). (b) consider the tangent plane to the surface z = x 2+xy−3y at the point (2, 3, 1). compute the angle of intersection between this plane and the plane from part (a

Step-by-step explanation:

Any 3 non collinear points would determine a unique plane. The four points given are:

P(0, 0, 1),Q (1, 2, 3), R(2, 4, 5), and S (4, 8, 11).

Direction ratios are listed below

PQ = 1,2,2

QR = 1,2,2

RS = 2,4,6

Hence we find that P,Q,R are collinear so let us select P,Q and S to determine the plane equation.

Hence we have plane equation

b) Given

Del w = (2x+y)i+(x-3)j-1k

At the point (2,3,1) normal would have direction ratios as

(7,-1,-1)

Hence tangent plane is

c) Angle of intersection would be the angle between normals

i.e. cos t = where t is the angle.

the cat is blue because the probability of extension towards the prefix of the diameter of the circle could only mathematically equal to the sum of the roots of the carrots from   your garden.

step-by-step explanation: