formulate either a symmetric equation or a parametric equations representing a l

Question

formulate either a symmetric equation or a parametric equations representing a line through the the point R and perpendicular to the line x(t)=2t-3, y(t)=-5t+3, z(t)=4t+11 formulate either a symmetric equation or a parametric equations representing a line through the the point R and perpendicular to the line x(t)=2t-3, y(t)=-5t+3, z(t)=4t+11 formulate either a symmetric equation or a parametric equations representing a line through the the point R and perpendicular to the line x(t)=2t-3, y(t)=-5t+3, z(t)=4t+11

Explanation / Answer

**The point R is not given ( its position vector).

iam mentioning method of solving.

given line

x(t)= a + tb

=(-3i + 3j + 11k) + t( 2I -5j+4k)

in parametric form

x(t)=2t-3, y(t)=-5t+3, z(t)=4t+11

suppose the required line passes through point(R)= ( x1,y1,z1).

so the line is passing through (2t-3, -5t+3, 4t+11 ) and ( x1,y1,z1)

direction of line (2t-3-x1, -5t+3-y1, 4t+11 -z1)

the line is perpendicular to (2t-3, -5t+3, 4t+11)

so dot product is zero.

(2t-3-x1, -5t+3-y1, 4t+11 -z1).(2t-3, -5t+3, 4t+11)=0

calculate value of t.

replace it in equation (2t-3-x1, -5t+3-y1, 4t+11 -z1)= (l,m,n)

equation of line in symmetric form is

(x-x1)/l = (y-y1)/m= (z-z1)/n

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