Plane

Which of the following equations describe a tangent plane to the curve z=1/ xy, at the point (x,y)=(1,2).a)z - 1/2 = -1/2(x-1) - 1/4(y-2)b)z - 1/2 = 1/2(x-1) + 1/4(y-2)c) z - 1/2 = 1/4(x-1) +... more

Which of the following is a plane that is parallel to the plane 2𝑥 − 2𝑦 − 2𝑧 = −2?(x,y,z) = (1,2,3) + t1(1,1,0) + t2(1,0,1)(x,y,z) • (2,2,2) = -2 (x,y,z) = (2,-2,-2)4x - 4y = -4 -4z

 A turbo-jet flies 50mph faster than a super-prop plane. If a turbo-jet goes 2000mi in 3 hr less time than it takes the super-prop to go 2800 mi, find the speed of each plane

With respect to the origin O, the lines l and m have vector equations r = 2i + k + λ(i − j + 2k) and r = 2j + 6k + µ(i + 2j − 2k) respectively. Find the equation of the plane which is parallel to l... more

use cylindrical coordinates to evaluate the triple integral that gives the mass the solid lying under the cone z=10-√(x2+y2), and above the xy-plane, if the density p is given by p(x,y,z)=x2+y2+z2.... more

3 distinct lines contained within a plane separate the plane into distinct regions. How many possible distinct regions of the plane may be separated by any 3 such lines?

Against the wind a commercial airline in South America flew 510miles in 3hours. With a tailwind the return trip took 2.5hours. What was the speed of the plane in still? air? What was the speed of... more

Find the line orthogonal to plane spanned by vector v= i-5j and vector 3k passing through (2,3,1)

If a jet plane is traveling 100mph faster than a propeller plane and then jet plane travels 6300 miles in 4 hours then how fast is each plane traveling

Let v1= [1,2,-1], v2=[-2,-1,1], and y=[4,-1,h].  For what value of h is y in the plane spanned by v1 and v2?

let v1=[1,2,-1]  v2=[-2,-1,1] and y=[4,-1,h]   For what value of h is y in the plane spanned by v1 and v2? h=?

Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -3.

Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way

Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way