Thank you for helping me solve All the questions above Find

Thank you for helping me solve All the questions above.

Find a parametric equation for the line that passes through the two points (0 1 2) and (3 3 2). Also, find the intersection of this line with the plane x + y + z = 1. Is the collection linearly dependent, or independent? Justify. {(3 2), (-1 -1), (1 -2)} Is the collection linearly dependent, or independent? Justify. {(1 1 0), (0 3 2), (0 1 1)} Describe geometrically the following sets as points, lines, planes, or all of R^n. {(x_1 x_2): 2x_1 + 3x_2 = 1, -x_1 + x_2 = 3} span{(1 1 2), (0 1 -1), (-1 0 2)} span{(1 1 2), (0 1 4), (-1 0 2)}

Solution

v1 = (0,1,2)

v2 = (3,3,2)

coordinates of the vector formed by these point

v = v2 - v1

v = (3 - 0, 3 - 1, 2 - 2)

v = (3, 2, 0)

Now the parametric equation will be

x = 3 + 3t, y = 3 + 2t, z = 2 + 0*t

x = 3 + 3t, y = 3 + 2t, z = 2

Now to find the intersection with the plane

x + y + z = 1

using the parametric equation

3 + 3t + 3 + 2t + 2 = 1

5t + 8 = 1

5t = -7

t = -7/5 = -1.4

Point of intersection will be

x = 3 - 3*1.4

y = 3 - 2*1.4

z = 2

point = (x, y, z) = (-1.2, 0.2, 2)

Please ask rest of the questions as different new questions, as they are not related to the first question. I will be happy to help.

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