Question

Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d =|axb|/|b|
where a = QR and b = QP. Use the above formula to find the distance from the point to the given line. (0,1,1); x = 3t, y = 4 - 3t, z = 1 + t

Answer 1

The distance from the point P(0,1,1) to the line L is about 3.61.

To find the distance from a point P(0,1,1) to a line L, we can put the coordinates of P and the parametric equation of the line L into the expression d = |axb|/|b| put in.

First, we need to find the vector a going from Q to R. You can find the Q and R coordinates using the line parametric equations. Putting t = 0 into the equations for x and y shows that Q is at the point (0,4,1). Setting t = 1 shows that R is at the point (3,1,2). So the vector a going from Q to R is <3>.

Now we need to find the vector b going from Q to P. Using the coordinates of Q and P, we know that b is a vector <-3,3,0>.

Substituting these vectors into the formula gives:

d = |<3> x <-3,3,0>|/|<-3,3,0>|

= |<9>|/|<-3,3,0>|

= |<9>|/sqrt(9+9)

=square(81+81+9)/square(18)

=square(171)/square(18)

= square (171/18)

= about 3.61

So the distance from the point P(0,1,1) to the line L is approximately 3.61.

Read more about this at brainly.com/question/15427716

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