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Calculating the angle of the triangle, prove that the points A(3, 4, -1) , B(1, 5, 1) and C(1, 2, -2) are the vertices of an isosceles triangle.

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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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