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Let vec a is any vector than what is the...

Let `vec a` is any vector than what is the value of `(vec a.hat i)hat i+(vec a.hat j)+(vec a.hat k)hat k` ?

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For an vector vec(r) = x hat(i) + y hat(j) + z hat(k) , prove that vec(r) = (vec(r). hat(i))hat(i) + (vec(r).hat(j))hat(j) + (vec(r) .hat(k)) hat(k)

Find a unit vector in direction of vec a-vec b , when vec a = 4 hat i + 7 hat j + hat k and vec b =3 hat j-11 hat k .

Find the scalar projection of the vector vec a= 3 hat i+6 hat j+9 hat k on vec b= 2 hat i+2 hat j-hat k .

Obtain the volume of the parallelopiped whose sides are vectors vec a= 2 hat i - 3 hat j + 4 hat k , vec b= hat i +2 hat j - hat k , vec c= 3 hat i - hat j +2 hat k . Also find the vector (vec a×vec b)×vec c .

MODERN PUBLICATION-VECTOR-EXERCISE
  1. Find the unit vector perpendicular to i + j and i + k.

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  2. If vec a × vec b = vec b × vec c != 0, Prove that vec a + vec c = m ve...

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  3. Let vec a is any vector than what is the value of (vec a.hat i)hat i+(...

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  4. What is the value of (hat i+hat j)×(hat j+hat k).(hat k+hat i)?

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  5. If vec Avec C and vec Bvec D are the diagonals of the parallelogram AB...

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  6. Find the area of the parallelogram whose adjacent sides are gives by t...

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  7. If vec(a) and vec(b) are two vectors such that |vec(a) + vec(b)| = |ve...

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  8. Determine the area of parallelogram whose adjacent sides are the vecto...

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

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

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

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

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

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

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

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

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

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

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

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

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