Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (3, 5, 0) and perpendicular to bot

Question

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (3, 5, 0) and perpendicular to both i + j and j + k x(t), y(t), z(t) = The symmetric equations are given by −(x − 3) = y − 5 = z. x + 3 = −(y + 5), z = 0. x − 3 = y − 5 = −z. x + 3 = −(y + 5) = z. x − 3 = −(y − 5) = z.

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Amelia 2 weeks 2021-09-09T09:13:26+00:00 1 Answer 0

Answers ( )

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    2021-09-09T09:15:13+00:00

    Answer:(x-3)=-(y-5)=z

    Step-by-step explanation:

    Given

    the point through which line passes is (3,5,0)

    so we need a vector along the line to get the equation of line

    It is given that line is perpendicular to both i+j & j+k

    therefore their cross product will give us the vector perpendicular to both

    v=(i+j)\times (j+k)=i-j+k

    therefore we get direction vector of line so we can write

    \frac{x-3}{1}=\frac{y-5}{-1} =\frac{z-0}{1}=t

    i.e.

    x=t+3,y=-t+5,z=t

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