Find the equation of the plane through the point

Assignment Help Engineering Mathematics

Reference no: EM132313541 , Length: 58 pages

Question 1: Prive that the point A(-1,6,6),B(-4,9,6),C(0,7,10) form the vertices of a right angled tringled.

Question 2: Derivation Of Distance Formula

Question 3: Derive the division formula

Question 4: External Division Formula

Question 5: Find the ratio in which the line segment joining points (4,3,2) and (1,2,-3) is divided by the co ordinate planes.

Question 6: Direction Cosine and Direction Ratio

Question 7: Property Of Direction Cosine

Question 8: Direction Ratio

Question 9: Exceptional cases:

Question 10: Finding Direction Cosine from Direction Ratio

Question 11: Direction Ratio of the line segment joining two points

Question 12: Angle between two lines with given Direction ratio

Question 13: Find the direction cosine of the line which is perpendicular to the lines whose direction ratios are <1,-2,3> and <2,2,1>

Plane

Question 14: Find the equation of the plane through the point (1,3,4), (2,1,-1) and (1,-4,3).

Equation Of plane in normal form

Question 15: Obtain the normal form of equation of the plane 3x+2y+6z+1 = 0 and find the direction cosine and length of the perpendicular from the origin to this plane.

Question 16: Distance Of a point from a plane

Question 17: Find the distance d from the point P(7,5,1) to the plane 9x+3y-6z-2 = 0

Question 18: Find the angle θ between the plane 4x-y+8z+7 =0 and x + 2y-2z+5 = 0

Question 19: Equation Of plane passing through three given point

Question 20: Find the equation of the plane determined by the point P₁(2, 3, 7) P₂(2, 3, 7) P₃(2, 3, 7)

Exercise

1. Write the equation of the plane perpendicular to N = 2i-3j+5k and passing through the point (2,1,3)

2. Parallel to the plane 3x-2y-4z = 5 and passing through (2,1,-3)

3. Passing through the (3,-2,-1)(-2,4,1)(5,2,3)

4. Find the perpendicular distance from 2x-y+2z+3 = 0

5. Find the perpendicular distance from 4x-2y+z-2 = 0

6. Find the cosine of the acute angle between each pair of plane 2x+2y+z-5 = 0 , 3x-2y+6z+5 = 0

7. Find the cosine of the acute angle between each pair of plane 4x-8y+z-3 = 0, 2x+4y-4z+3 = 0

Sphere

Problems

1. Find the equation of the sphere through the point (2,0,1), (1,-5,-1), (0,-2,3) and (4,-1,2).

Also find its centre and radius

2. Obtain the equation of the sphere passing through the origin and the points (a,0,0), (0,b,0) and (0,0,c).

3. Find the equation of the sphere whose diameter is the line joining the origin to the point (2, -2, 4)

Reference no: EM132313541

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