Find the point of intersection of lines /1 and 12. h:1 = (5+ 2t1)i+ (53 - 13t1 ) j + 2t1k 12:12 = (3 + 2t2) i+ (11 - 2t2) j + (13 - t2) k (Give your answer in the form (*, *, *). Express numbers in exact form. Use symbolic notation and fractions 31 55 16 ( x, y, Z) = 3 ' 3 ' 3 Incorrect Find the angle 0 between / 1 and 12. (Express numbers in exact form. Use symbolic notation and fractions where needed.)When two planes intersect, the angle between the planes is defined as the non-obtuse angle between their normals. If N, and N2 are the normals of two intersecting planes, the angle 0 between these planes is given by cos(0) = IN1 . Nal OSOS Find the angle 0 between two intersecting planes x - 3y + 3z = 8 and 2x - y + 5z = 7. (Express numbers in exact form. Use symbolic notation and fractions where needed.) 0 =Two unidentified flying objects are at the points (4t, -4t, 4 - 4t) and (4t - 32, 4t, 6t - 4) at time t, t 2 0. Find the acute angle between the paths. (Express numbers in exact form. Use symbolic notation and fractions where needed.) -1 -9 0 = COS V 195 Incorrect Find where the paths intersect (or determine that they do not). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *, *). Enter DNE if the paths do not intersect.)Explain why the set of points (x, y, z) equidistant from (3, 5, 0) and (-3, 3, 8) is a plane. Select the correct explanation. Because in two dimensions, the set of points equidistant from two points is a line, and the result of rotating it through the third dimension with respect to the segment between the points is a plane. O Because in two dimensions, the set of points equidistant from two points is a plane. O Because in two dimensions, the set of points located at a distance r from the two points is a line, and considering all possible values of r produces a plane. O Because in three dimensions, each point on a plane is equidistant from a given point, so that if the distances from both points are equal, the plane is equidistant from both points. Find the equation of this plane. Hint: This can be done in two ways. The first one is to use the distance formula to equate the distances between (x, y, z) and the given points, simplifying the result to obtain the equation of the plane. The second one is to find a point on the plane and a vector normal to the plane and use the answer to find the equation of the plane. (Express numbers in exact form. Use symbolic notation and fractions where needed.)Let P = (2, 5, 3), Q = (1, 3,0), R = (-2, -1, 5). Find the area of the parallelogram with one vertex at P and sides PQ and PR. (Use symbolic notation and fractions where needed.) area: V780 Incorrect