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Show that the line joining the origin to...

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

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Show that the line through the points (1, – 1, 2), (3, 4, – 2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Find the equation of the plane passing through the point (3,-3, 1) and perpendicular to the line joining the points (3, 4, - 1) and (2, - 1,5). Also find the coordinates of the foot of the perpendicular, the equation of the perpendicular line and the length of perpendicular drawn from the origin to the plane.

Determine the value of k so that the lie joining the points A(k,1,-1), B(2,0,2k) is perpendicular to the line joining the points C(4,2k,1) and D(2,3,2)

Find the equation of the plane passing through the point A(1, 2, 1) and perpendicular to the line joining the points P(1, 4, 2) and Q(2, 3, 5). Also, find the distance of this plane from the line (x+3)/(2)=(y-5)/(-1)=(z-7)/(-1)

Show that the line joining (2, -3) and (- 5,1) is : perpendicular to the line joining (4, 5) and (0, - 2).

Find the vector and cartesian equation of a line through the point (1, – 1, 1) and perpendicular to the lines joining the points (4, 3, 2), (1, -1,0) and (1, 2,-1), (2, 1, 1).

Show that the line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (– 1, – 2, 1), (1, 2, 5).

Find the equation of the plane passing through the points (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5), Also, find the perpendicular distance of the plane from the origin.

Show that the line : through (2, - 3) and (-1, 2) is perpendicular to the line joining (3, 7) and (- 2, 4).

Find the coordinates of the point where the line through the points A (3, 4, 1) and B (5, 1, 6) crosses the plane determined by the points P (2, 1, 2), Q(3, 1, 0) and R (4, -2,1)

NAND LAL PUBLICATION-INTRODUCTION TO GRAPHS -ADDITIONAL QUESTIONS FOR PRACTICE (Objective Type Questions)
  1. The point of intersection of axis is called …………. .

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  2. The two axes divide the plane into 4 parts called underline("")...

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  3. The ordinate of a point on x - axis is underline("").

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  4. State whether True or False.Correct that are false. The co-ordinates o...

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  5. The coordinates of a point on the lin y = x where perpendicular dista...

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  6. The y- ordinate of a point is also called underline("").

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  7. State whether the following statements are true or false . ...

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  8. Point (0,0) lies on both axes .

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  9. Show that the line joining the origin to the point (2, 1, 1) is perpen...

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  10. X- axis is a horizontal line .

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  11. The point of intersection of axis is called …………. .

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  12. Any point on y- axis has its y- ordinate zero .

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  13. In a cartesian plane x - axis and y- axis are together called...

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  14. Which graph is incorrect

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  15. Which graph is incorrect

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  16. Which graph is incorrect

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  17. The horizontal axis called (i) x - axis , (ii) y- axis ...

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  18. The ordinate of point (7,5) marked on the graph is (i) 7 (...

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  19. The co -ordinates of a point are (2,0) . It lies on (i) y- ...

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  20. A point lies on y - axis if its (i) x - coordinate is 0 ...

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