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Prove that the vectors 2hat(i) - hat(j) ...

Prove that the vectors `2hat(i) - hat(j) + hat(k), hat(i) - 3hat(j) - 5hat(k), 3hat(i) - 4hat(j) - 4hat(k)` are the sides of a right angled triangle.

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Show that the vectors -hat(i) + hat(j) - hat(k), hat(i) + hat(j) + hat(k) and hat(i) + hat(k) are coplanar.

Show that the vectors vec(a) = 3hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) - 3hat(j) + 5hat(k) and vec(c) = 2hat(i) + hat(j) - 4hat(k) form a right angled triangle.

Show that the following vectors are coplanar. hat(i) - 2hat(j) + 2hat(k), 3hat(i) + 4hat(j) + 5hat(k), -2hat(i) + 4hat(j) - 4hat(k)

Show that the following vectors are coplanar. hat(i) + 2hat(j) + 3hat(k), -2hat(i) - 4hat(j) + 5hat(k), 3hat(i) + 6hat(j) + hat(k)

Show that the vectors 2hat(i) + 3hat(j), 5hat(i) - 5hat(k) and 6hat(j) + 4hat(k) are coplanar.

Show that the vectors 2hat(i)-3hat(j)+4hat(k) and -4hat(i)+6hat(j)-8hat(k) are collinear.

Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

ARIHANT PUBLICATION-VECTOR ALGEBRA -Odisha Bureau.s Textbook Solutions (Exericise 12(a))
  1. In each of the following find the vector vec(PQ), its magnitude and di...

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  2. In each of the following find the vector vec(PQ), its magnitude and di...

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  3. If a = (2, -2, 1), b = (2, 3, 6) and c = (-1, 0, 2) find the magnitude...

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  4. Determine the unit vector having the direction of the given vector in ...

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  5. Determine the unit vector having the direction of the given vector in ...

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  6. Determine the unit vector having the direction of the given vector in ...

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  7. Determine the unit vector having the direction of the given vector in ...

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  8. Find the unit vector in the direction of the vector r(1) - r(2), where...

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  9. Find the unit vector parallel to the sum of the vectors veca = 2hati+4...

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  10. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  11. The position vectors of the points A, B, C and D are 4hati+3hatj-hatk,...

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  12. In each of the following problems, show by vector method that the give...

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  13. In each of the following problems, show by vector method that the give...

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  14. Prove that the vectors 2hat(i) - hat(j) + hat(k), hat(i) - 3hat(j) - 5...

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  15. Prove by vector method that the medians of a triangle are concurrent.

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  16. Prove by vector method that the diagonals of a parallelogram bisect ea...

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  17. Prove by vector method that the line segment joining the mid points of...

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  18. Prove by vector method that the lines joining the mid points of consec...

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  19. Prove by vector method that in any triangle ABC, the point P being on ...

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  20. Prove by vector method that in a parallelogram, the line joining a ve...

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