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 \(d = \frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}|}\) where \(\mathbf{a} = \overrightarrow{QR}\) and \(\mathbf{b} = \overrightarrow{QP}\). Use the above formula to find the distance from the point to the given line. \((5, 2, -1);\) \(x = 2 + t,\) \(y = 2 - 3t,\) \(z = 4 - 2t\) \(d = \frac{\sqrt{706}}{\sqrt{35}}\)

          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
\(d = \frac{|\mathbf{a} \times \mathbf{b}|}{|\mathbf{a}|}\)
where \(\mathbf{a} = \overrightarrow{QR}\) and \(\mathbf{b} = \overrightarrow{QP}\).
Use the above formula to find the distance from the point to the given line.
\((5, 2, -1);\) \(x = 2 + t,\) \(y = 2 - 3t,\) \(z = 4 - 2t\)
\(d = \frac{\sqrt{706}}{\sqrt{35}}\)

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 = (|𝐚×𝐛|)/(|𝐚|)
where 𝐚 = QR and 𝐛 = QP.
Use the above formula to find the distance from the point to the given line.
(5, 2, -1); x = 2 + t, y = 2 - 3t, z = 4 - 2t
d = (√(706))/(√(35))

Added by Tammy C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert William Semus

05/06/2022

Step 1

Q = (2, 2, 4) R = (2 + 1, 2 - 3, 4 - 2) = (3, -1, 2) a = QR = (3 - 2, -1 - 2, 2 - 4) = (1, -3, -2) Show more…

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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=Ia x bI |a] where a = QR and b = QP Use the above formula to find the distance from the point to the given line 5,2,-1x=2+t,y=2-3t,z=4-2t V706 =p V35 X