Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t How would I go about doing this question?
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Originally Posted by IanCarney Determine the value of c such that the plane with equation 2x+3y-cz-8=0 is parallel to the line with equation x=1+2t, y=2+3t, z=-1+t A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane.
Originally Posted by Plato A line is parallel to a plane if and only if its direction vector is perpendicular to the normal of the plane. Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value?
Originally Posted by IanCarney Direction vector: (2,3,1) and the normal of the plane is (2,3, c), right? What would I do now? Cross product? But how would I find the c value? Cross products are not in play here. Two vectors are perpendicular it their dot product is zero.