Find a vector equation of the plane in R containing the two lines (t) = (2,-1,...

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Find a vector equation of the plane in R³ containing the two lines (t) = (2,-1, 4)+ t(5,3,-1) and l2(t) = (2,-1,4)+(2,0,-3), (2 points) Find a normal equation of the hyperplane in R5 perpendicular to the vector (2,-1,7,9,5) and passing through the point (3, 2, 1, 1.-4). Does it pass through origin? (1+1 point) In R¹, consider the hyperplanes H₁ given by the equation x-y+2:+w= 0 and H₂ given by -3x+3y-6z-3w=3. Are the two hyperplanes parallel? Find the "minimum" distance between them. (3 points) Find the distance of the point (2,3,4) from the plane z+y+z= 1. Give the equation of the line passing through this point along the normal vector. (3 points) Find a vector equation of the plane in R³ containing the two lines (t) = (2,-1, 4)+ t(5,3,-1) and l2(t) = (2,-1,4)+(2,0,-3), (2 points) Find a normal equation of the hyperplane in R5 perpendicular to the vector (2,-1,7,9,5) and passing through the point (3, 2, 1, 1.-4). Does it pass through origin? (1+1 point) In R¹, consider the hyperplanes H₁ given by the equation x-y+2:+w= 0 and H₂ given by -3x+3y-6z-3w=3. Are the two hyperplanes parallel? Find the "minimum" distance between them. (3 points) Find the distance of the point (2,3,4) from the plane z+y+z= 1. Give the equation of the line passing through this point along the normal vector. (3 points)

Answer rating: 100% (QA)

To find a vector equation of the plane in R 3 containing the two lines l 1 t 214 t531 and l 2 t 214 t203 we need to first find the normal vector to the plane This can be done by taking the cross produ... View the full answer