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Determine k such that a vector vec(r) is...

Determine k such that a vector `vec(r)` is at right angles to each of the vectors `vec(a) = k hat(i) + hat(j) + 3hat(k), vec(b) = 2hat(i) + hat(j) - k hat(k)` and `vec(c) = -2hat(i) + k hat(j) + 3hat(k)`.

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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.

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.

MODERN PUBLICATION-VECTOR-EXERCISE
  1. Determine the area of parallelogram whose adjacent sides are the vecto...

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  2. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  3. Prove that (vec a × vec b).(vec c × vec d) = [[vec a.vec c,vec a.vec d...

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  4. Find a unit vector in direction of vec a-vec b, when vec a = 4 hat i +...

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  5. If vec a and vec b be perpendicular vectors, then prove that (vec a + ...

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  6. Find the value of lambda so that the three vectors are co-planar. (2,-...

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  7. Determine k such that a vector vec(r) is at right angles to each of th...

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  8. Find the scalar and vector projection of veca on vecb. veca = hati+hat...

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  9. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  10. Prove that : |veca + vecb|le|veca|+|vecb|.

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  11. Show that vec a × (vec b+vec c) + vec b × (vec c+vec a) + vec c × (vec...

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  12. If vec(a) and vec(b) are unit vectors, then what is the angle between ...

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

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

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  15. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  16. Prove the following by vector method. Median to the base of an isoscel...

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  17. Prove the following by vector method. The diagonals of a rhombus are a...

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  18. Prove the following by vector method. An angle inscribed in a semi-cir...

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  19. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  20. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

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