See attached image. Please show detailed steps with explanation if possible. Find a vector equation for the linethrough the point Pla,-1,0,3 thatis orthogondl t the hyperplane-3x,+X+2x3-Xy=7

Answered: Find a vector equation for the line…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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See attached image. Please show detailed steps with explanation if possible.

Find a vector equation for the line
through the point Pla,-1,0,3 that
is orthogondl t the hyperplane
-3x,+X+2x3-Xy=7

Expert Solution

Step 1

Suppose a line passing through the fixed point with position vector $a$ and parallel to vector $b$ , then vector equation of a line is $r = a + λ b$ , where $λ$ is an arbitrary constant.

Consider an equation of plane in $4 d$ is $a x_{1} + b x_{2} + c x_{3} + d x_{4} = e$ . It is also be called hyperplane according to its higher dimension that is 5d. The vector $<a, b, c, d>$ is normal vector to the plane.

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