Consider the following planes. x + y + z = 7, x + 3y + 3z =...

Consider the following planes.

x + y + z = 7, x + 3y + 3z = 7

(a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.)
(x(t), y(t), z(t)) =

(b) Find the angle between the planes. (Round your answer to one decimal place.)
°

Expert Solution

a) Steps to find the parametric equation of line of intersection of two planes.

Step-1.Read off normal vectors of planes n1and n2

Step-2. Find directional vector d parallel to the line by taking cross product of two normal vectors.

Step -3 Find one point on line by taking z =0 and then solving two equation.

Step-4 Then use the formula for equation of line

r(t) = r0 + d*t

(b)Steps to find angle between two planes.

Step-1 Take dot product of normal vectors found in part a.

(n1).(n2) = |n1|*|n2| cos( theta)

step-2. Calculate theta from above equation.

milcah answered 1 year ago

Given two planes 2x - y + z = 7 and x + 3y - 4z...

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