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.

The parametric form of the equation is;

The symmetric form of the equation is .

Given

The line through (3, 5, 0) and perpendicular to both i + j and j + k

Where the value of .

To find a, b, c by evaluating the product of ( i + j) and ( j + k ).

The value of a = 1, b = -1 and c = 1.

Substitute all the values in the equation.

Therefore,

The parametric form of the equation is;

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(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

=t

i.e.

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

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times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

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step-by-step explanation: