Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 7, 8) and R(−1, 5, 6).

Therefore, the distance from the point P(1, 1, 1) to the line through QR is 4.068.

Step-by-step explanation:

We have the point P(1, 1, 1) to the line through Q(0, 7, 8) and R(−1, 5, 6).

Equation for line through PQ is

r= (0·i +7j+8k)+t ((-1-0)i +(5-7)j+ (6-8)k)

r=(7j+8k)+ t(-i-2j-2k)

We calculate the point T on line through RQ

T=\left[\begin{array}{ccc}T1\\T2\\T3\end{array}\right] =

\left[\begin{array}{ccc}0\\7\\8\end{array}\right] + t ·\left[\begin{array}{ccc}-1\\-2\\-2\end{array}\right]

T=\left[\begin{array}{ccc}T1\\T2\\T3\end{array}\right] =\left[\begin{array}{ccc}-t\\7-2t\\8-2t\end{array}\right]

PT=T-P = \left[\begin{array}{ccc}-t\\7-2t\\8-2t\end{array}\right] - \left[\begin{array}{ccc}1\\1\\1\end{array}\right]

PT=\left[\begin{array}{ccc}-1-t\\6-2t\\7-2t\end{array}\right]

Since PT is perpendicular to given line, then

\left[\begin{array}{ccc}-1-t\\6-2t\\7-2t\end{array}\right] · \left[\begin{array}{ccc}-1\\-2\\-2\end{array}\right]=0

we get

1+t-12+4t-14+4t=0

t=25/9

we have

PT=\left[\begin{array}{ccc}-1-t\\6-2t\\7-2t\end{array}\right]

PT=\left[\begin{array}{ccc}-34/9\\4/9\\13/9\end{array}\right]

We get that the distance from the point P(1, 1, 1) to the line through QR is

PT=\sqrt{(-34/9)^2 + (4/9)^2 + (13/9)^2}

PT=4.068

Therefore, the distance from the point P(1, 1, 1) to the line through QR is 4.068.

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

70.30

step-by-step explanation: