Vecttor
3D-PLANES
1-MARK
1.Find the angle between the line x + 1 = y – 1 = z – 2 and the plane 2x + y – 3z = 4. 2 -1 3
2 Find the distance of the point (1, 2, 0) from the plane 4x + 3y + 12z = 16.
3.Find the equation of the line passing through the point with position vector 4i – j + 3k and perpendicular to the plane r.(6i – 3j + 7k) + 2 = 0.
4. If the points (1, 2, p) and (-3, 0, -1) be equidistant from the plane r.(3i + 4j – 12k) + 17 = 0 then find ‘p’.
5. Find the vector and Cartesian equation of plane passing through the intersection of two planes r.(i + j + k) = 6 and r.(2i + 3j + 4k) = -5 and the point (1, 1, 1).
6. Find angle between line r=2i-j+3k +ג (3i-j+2k) and plane r.(i+j+k)=3.
7. Write the equation of plane passing through (1,2,3) and perpendicular to line [pic] in vector form .
8.Find the equation of the plane through the point (2,3,4) and parallel to the plane r.(2i-3j+5k)+7=0.
9. Find the equation of the line passing through the point with position vector 4i – j + 3k and perpendicular to the plane r.(6i – 3j + 7k) + 2 = 0
10.Find distance of origin from plane 3x+4y-z+7=0.
4/6MARKS
1.Find the length and foot of perpendicular from the point (1,1,2) to the plane [pic]
2.Find the foot of perpendicular from (1,2,3) to the line [pic] Also obtain the equation of plane containing the line and the point (1,2,3)
3.Prove that the image of the point ( 3, -2, 1 ) in the plane 3x – y + 4z = 2 lies on the plane,
x + y + z + 4 =0
4.Find the distance of the point ( 3,4,5) from the plane x +y+z=2 measured parallel to the line 2x = y = z
5.Show that the lines [pic] and [pic] are coplanar . Also find the eq of the plane containing the lines.
6.Find the eq of the plane thro’ the points (3,4,2)&(7,0,6) and is perpendicular to the plane 2x – 5y = 15
7.Find the eq of the plane passing through the points [pic]and [pic]
1-MARK
1.Find the angle between the line x + 1 = y – 1 = z – 2 and the plane 2x + y – 3z = 4. 2 -1 3
2 Find the distance of the point (1, 2, 0) from the plane 4x + 3y + 12z = 16.
3.Find the equation of the line passing through the point with position vector 4i – j + 3k and perpendicular to the plane r.(6i – 3j + 7k) + 2 = 0.
4. If the points (1, 2, p) and (-3, 0, -1) be equidistant from the plane r.(3i + 4j – 12k) + 17 = 0 then find ‘p’.
5. Find the vector and Cartesian equation of plane passing through the intersection of two planes r.(i + j + k) = 6 and r.(2i + 3j + 4k) = -5 and the point (1, 1, 1).
6. Find angle between line r=2i-j+3k +ג (3i-j+2k) and plane r.(i+j+k)=3.
7. Write the equation of plane passing through (1,2,3) and perpendicular to line [pic] in vector form .
8.Find the equation of the plane through the point (2,3,4) and parallel to the plane r.(2i-3j+5k)+7=0.
9. Find the equation of the line passing through the point with position vector 4i – j + 3k and perpendicular to the plane r.(6i – 3j + 7k) + 2 = 0
10.Find distance of origin from plane 3x+4y-z+7=0.
4/6MARKS
1.Find the length and foot of perpendicular from the point (1,1,2) to the plane [pic]
2.Find the foot of perpendicular from (1,2,3) to the line [pic] Also obtain the equation of plane containing the line and the point (1,2,3)
3.Prove that the image of the point ( 3, -2, 1 ) in the plane 3x – y + 4z = 2 lies on the plane,
x + y + z + 4 =0
4.Find the distance of the point ( 3,4,5) from the plane x +y+z=2 measured parallel to the line 2x = y = z
5.Show that the lines [pic] and [pic] are coplanar . Also find the eq of the plane containing the lines.
6.Find the eq of the plane thro’ the points (3,4,2)&(7,0,6) and is perpendicular to the plane 2x – 5y = 15
7.Find the eq of the plane passing through the points [pic]and [pic]