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If a line makes angle 90o, 60oand 30owi...

If a line makes angle `90o`, `60o`and `30o`with the positive direction of x, y and z-axis respectively, find its direction cosines.

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NAVNEET PUBLICATION - MAHARASHTRA BOARD-QUESTION BANK 2021-VECTOR AND THREE DIMENSIONAL GEOMETRY
  1. If the vectors 2 hat(i) - q hat(j) + 3 hat(k) and 4 hat(i) - 5 hat(j)...

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  2. Find bar(a). bar(b) xx bar(c), if bar(a) = 3 hat(i) - hat(j) + 4 hat(k...

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  3. If a line makes angle 90o, 60oand 30owith the positive direction of ...

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  4. The vector bar(a) is directed due north and |bar(a)| = 24. The vector ...

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  5. Show that following points are collinear P(4, 5, 2), Q(3, 2, 4), R(5, ...

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  6. If a vector has direction angles 45^(@) and 60^(@) find the third dire...

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  7. If bar(c) = 3 bar(a) - 2 bar(b) then prove that [(bar(a),bar(b),bar(c...

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  8. If |bar(a).bar(b)| = |bar(a) xx bar(b)| & bar(a). bar(b) lt 0, then fi...

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  9. The direction ratios of a vector perpendicular to the two lines whose ...

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  10. If bar(a), bar(b) and bar(c) are position vectors of the points A, B, ...

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  11. If bar(a) and bar(b) are two vectors perpendicular each other, prove t...

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  12. Find the position vector of point R which divides the line joining the...

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  13. Find a unit vector perpendicular to the vectors hat(j) + 2 hat(k) & ha...

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  14. If two of the vertices of the triangle are A(3, 1, 4) and B(-4, 5, -3)...

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  15. Find the centroid of tetrahedron with vertices K(5, -7, 0), L(1, 5, 3)...

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  16. If a line has the direction ratios 4, -12, 18, then its direction cos...

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  17. Show that the points A(2, -1, 0) B(-3, 0, 4), C(-1, -1, 4) and D(0, -5...

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  18. Using properties of scalar triple product, prove that [(bar(a) + bar(b...

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  19. The direction ratios of AB are -2,2,1. If A -= (4,1,5) and l(AB) = 6 u...

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  20. If G(a,2,-1) is the centroid of the triangle with vertices P(1,3,2),Q(...

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