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Using direction ratios prove that the po...

Using direction ratios prove that the points (4, 2, -6), (5, -3, 1), (12, 4, 5) and (11, 9, -2) taken in order are the vertices of a rectangle.

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Using direction numbers show that points P(4, 7, 8) and Q(2, 3, 4), R(-1, -2, 1) and S(1, 2, 5) taken in order, are the vertices of a parallelogram. Is the parallelogram a rectangle?

Prove that the points (-7, -3), (5, 10), (15, 8) and (3, -5) taken in order are the corners of a parallelogram.

Prove that the points A(-5 , 1 , 1) , B(1 , 3 , 4) , C ( - 1 , 6 , 10) and D (-7 , 4, 7) taken in order are the vertices of a rhombus .

Prove that the points ( 2 , 3, 5) , ( - 4 , 7 , - 7) , ( - 2 , 1 , -10) and ( 4 , - 3 , 2) are the vertices of a rectangle .

Show that the points A(7, 3), B(6, 1), C(8, 2) and D(9, 4) taken in that order are vertices of a parallelogram.

Using direction ratio show that the points (2, 6, 3), (1, 2, 7) and (3, 10, -1) are collinear.

Prove that the points ( 4 , 7 , 6) , ( 2 , 3 , 2 ) , ( - 1, -2, -1) and ( 1, 2 , 3) taken in order are the vertices of a parallelogram . Is the the parallelogram a rectangle?

Using direction ratios show that the points P(2, 3, 4) Q(-1, -2, 1) and R(5, 8, 7) are collinear.

Using direction ratios show that the points (2,6,3),(1,2,7) and (3,10,-1) are collinear.

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CHHAYA PUBLICATION-DIRECTION COSINES AND DIRECTION RATIOS-Exercise 3 : Short Answer Type Questions
  1. Show that the staright line joining the points (-1, 0, -2) and (1, 3, ...

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  2. Prove that the straight line joining the points (4, 5, 0) and (5, 3, 3...

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  3. Calculating the angle of the triangle, prove that the points A(3, 4, -...

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  4. Find the acute angle between x-axis and the straight line joining the ...

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  5. Calculating direction ratios show that the triangle formed by joining ...

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  6. Straight lines OA and OB are drawn from the origin O, if the direction...

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  7. Find the coordinates of the foot of the perpendicular drawn from the p...

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  8. Determine the values of a and b for which the straight line joining th...

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  9. If the straight line joining the points (4, -3, 2) and (3, -1, 5) is p...

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  10. Find the acute angle between two straight lines whose direction number...

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  11. Let A(2, -3, -1), B(4, 5, 2), C(-3, 4, 1) and D(2, 3, 5) are four give...

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  12. Using direction ratios prove that the points (4, 2, -6), (5, -3, 1), (...

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  13. Using direction numbers show that points P(4, 7, 8) and Q(2, 3, 4), R(...

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  14. Let l(1), m(1), n(1) and l(2), m(2), n(2) be the direction ratios of t...

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  15. Let P(-9, 4, 5) and Q(11, 0, -1) be two given points. If O be the orig...

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  16. Let A(-2, 0, 3), B(0, 3, -3), C(3, 3, 5) and D(5, 4, 3) be four given ...

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  17. Find the acute angle between the two straight lines whose direction co...

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  18. Find the angle between the two straight lines whose direction cosines...

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  19. Find the angle between the two straight lines whose direction cosines...

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  20. Find the acute angle between the two straight lines whose direction co...

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