Acertain plane is described by 2x + 3y + 4z = 16. find the unit vector normal to the surface in the direction away from the origin.

the unit vector is u=(2/√29 ,3/√29,4/√29)

Step-by-step explanation:

From the plane equation

2x+3y+4z = 16

2x+3y+4*(z-4) =0

(2,3,4)*(x-0,y-0,z-4) =0

then the vector n=(2,3,4) is normal to the plane that contains the point (0,0,4)

the modulus of n will be

|n|= √(2²+3²+4²) = √29

then the unit vector will be

u=n/|n| = (2,3,4)/√29= (2/√29 ,3/√29,4/√29)

since there are 2 possible choices

(2/√29 ,3/√29,4/√29)  or  (-2/√29 ,-3/√29,-4/√29)

then the vector that points away from the origin is

(2/√29 ,3/√29,4/√29)

idk

step-by-step explanation:

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc