Consider three planes P=x-y+z= 1, P- x+y-z=-1 and P;: x- 3y + 3z = 2. La...

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Consider three planes P=x-y+z= 1, P- x+y-z=-1 and P;: x- 3y + 3z = 2. La and L be the lines of intersection of the planes P, and P3, P, and P, and P, and P2 respecitvely Statement -1: At least two of the lines L,, L, and L, are non-parallel. Statement -2: The three planes do not have a common point A Both the statement are true, and Statement 2 is the correct explanation for Statement 1 2) Both the statement are true, but Statement 2 is not the correct explanation for Statement1 3) Statement 1 is true and Statement 2 is false ) Statement 1 is false and Statement 2 is true. lat Consider the planes 3x- 6y – 2z = 15 and 2x + y- 2z = 5. Statement -1: The parametric equations of the line of intersection of the given planes are x= 3+ 14t, y = 2t, z = 15t Statement -2 : The vector 147+21+15k is parallel to the line of intersection of the given planes. 1) Both the statement are true, and Statement 2 is the correct explanation for Statement 1 gle 2) Both the statement are true, but Statement 2 is not the correct explanation for Statement1 3) Statement 1 is true and Statement 2 is false 4) Statement 1 is false and Statement 2 is true. Numerical value type questions 28. Consider, the lines L- and x-1 y +3,L2:- x-4 y+3 z+3 =-= and the planes P:7x+y+2z=3, %3D %3D 2 1 1 1 1 P:3x+5y-6z=4. Let ax+by+cz=Dd the equation of the plane passing through the point of intersection of lines L, and L, and perpendicular to planes P, and P,. then (a+d) – (b+c) = x-2 y+3 z+5 1 29. The point on the line at a distance of 6 from the point (2, -3, -5) is (a,B,Y) then %3D -2 -2 B+Y a+B eter . If the distance from point P(1, 1, 1) to the line passing through the points Q(0, 6, 8) and R (-1, 4, 7) is expressed in the form (p+q)(p+q-1) where and q are coprime, then the value Pl. The distance between the line = 2i – 2î + 3k + ^(î – j+4k) and the plane r (i+5j+k)= 5 is y $2. Two lines L:x= 5, and L2 :x= 0, =- -1 2-0 are coplanar. Then a can take value (s) %3D 3-a -2 O1,02 then a, +A2 = ELITE SERIO Consider three planes P=x-y+z= 1, P- x+y-z=-1 and P;: x- 3y + 3z = 2. La and L be the lines of intersection of the planes P, and P3, P, and P, and P, and P2 respecitvely Statement -1: At least two of the lines L,, L, and L, are non-parallel. Statement -2: The three planes do not have a common point A Both the statement are true, and Statement 2 is the correct explanation for Statement 1 2) Both the statement are true, but Statement 2 is not the correct explanation for Statement1 3) Statement 1 is true and Statement 2 is false ) Statement 1 is false and Statement 2 is true. lat Consider the planes 3x- 6y – 2z = 15 and 2x + y- 2z = 5. Statement -1: The parametric equations of the line of intersection of the given planes are x= 3+ 14t, y = 2t, z = 15t Statement -2 : The vector 147+21+15k is parallel to the line of intersection of the given planes. 1) Both the statement are true, and Statement 2 is the correct explanation for Statement 1 gle 2) Both the statement are true, but Statement 2 is not the correct explanation for Statement1 3) Statement 1 is true and Statement 2 is false 4) Statement 1 is false and Statement 2 is true. Numerical value type questions 28. Consider, the lines L- and x-1 y +3,L2:- x-4 y+3 z+3 =-= and the planes P:7x+y+2z=3, %3D %3D 2 1 1 1 1 P:3x+5y-6z=4. Let ax+by+cz=Dd the equation of the plane passing through the point of intersection of lines L, and L, and perpendicular to planes P, and P,. then (a+d) – (b+c) = x-2 y+3 z+5 1 29. The point on the line at a distance of 6 from the point (2, -3, -5) is (a,B,Y) then %3D -2 -2 B+Y a+B eter . If the distance from point P(1, 1, 1) to the line passing through the points Q(0, 6, 8) and R (-1, 4, 7) is expressed in the form (p+q)(p+q-1) where and q are coprime, then the value Pl. The distance between the line = 2i – 2î + 3k + ^(î – j+4k) and the plane r (i+5j+k)= 5 is y $2. Two lines L:x= 5, and L2 :x= 0, =- -1 2-0 are coplanar. Then a can take value (s) %3D 3-a -2 O1,02 then a, +A2 = ELITE SERIO

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