Vectors - Intersections of Planes?

Can someone please explain to me the steps involved to solve this. Thanks.





1) In what line does the plane n= -54x -55y +16z + 56 = 0 intersect the yz-plane.





Please answer in a vector equation in the form r = (x,y,z) + t(a,b,c)

Vectors - Intersections of Planes?
In what line does the plane n= -54x -55y +16z + 56 = 0 intersect the yz-plane.





This is the same as asking, find the line of intersection of the two planes:





-54x - 55y + 16z + 56 = 0


x = 0





The directional vector v, of the line of intersection will be orthogonal to the normal vectors of both planes. Take the cross product.





v = n1 X n2 = %26lt;-54, -55, 16%26gt; X %26lt;1, 0, 0%26gt; = %26lt;0, 16, 55%26gt;





Now find a point on the line. Let x = 0 and y = 0.





-54x - 55y + 16z + 56 = 0


16z + 56 = 0


16z = -56


z = -7/2





The point is P(0, 0, -7/2).





The equation of the line is:





r(t) = P + tv


r(t) = (0, 0, -7/2) + t%26lt;0, 16, 55%26gt;


where t is a scalar that ranges over the real numbers


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Reply:55y-16z=56 woud be the line but not sure abt how to represent in the vector form...hope u wd b noing it....