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Prove the following by vector method. Measure of the angle between two diagonals of a cube is `cos^-1 (1/3)`

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SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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

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  3. Prove the following by vector method. Measure of the angle between two...

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

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  5. if veca=2hati-5hatj+8hatk, vecb=hati-3hatj-7hatk and vecc=-3hati+2hatj...

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  6. If veca = 3hati+3hatj+hatk and vecb = -2hati+hatj-2hatk then what is t...

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  7. Find the angle between the vectors 3hati + 4hatj and 2hati+hatj+sqrt3h...

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  8. What is the angle between two vectors veca and vecb with magnitude 2 a...

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  9. If veca = 3hati+3hatj+hatk and vecb = -2hati+hatj-2hatk then what is t...

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  10. Find the component of the vector vec(b) = 8hat(i) + hat(j) in the dire...

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  11. What is the value of x so that the vector 6hati+2hatj-3hatk and hati-4...

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  12. Determine mu, for which the vector vec(a)=mu(6hat(i)+2hat(j)-3hat(k)) ...

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  13. How many directions a null vector has ?

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  14. If veca,vecb andvecc are three mutually perpendicular vectors, each of...

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  15. What is the volume of the parallelopiped whose sides are given by the ...

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  16. Write the values of m and n for which the vectors (m-1)overset^i+(n+2)...

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  17. Show that the vectors 2hati + 3hatj,5hati -5hatk and 6hatj + 4hatk are...

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  18. If A, B, C, D, E are the.vertices of a regular pentagon, find the vect...

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  19. If vec(a).vec(b) = 0 and vec(a) xx vec(b) = vec(0), then draw the conc...

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  20. Find a vector in the direction of vector 2hati-3hatj+6hatk which has m...

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