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Prove that (veca+vecb).(veca+vecb)=|vec...

Prove that
`(veca+vecb).(veca+vecb)=|veca|^2+|b|^2` if and only if `veca,vecb` are perpendicular, given
`veca!=vec0"and"vecb!=0`.

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V PUBLICATION-VECTOR ALGEBRA-QUESTION BANK
  1. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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

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  3. Prove that (veca+vecb).(veca+vecb)=|veca|^2+|b|^2 if and only if veca...

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  4. Choose the correct answer. If theta is the angle between two vectors v...

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  5. Let 'veca' and 'vecb' be two unit vectors and 'theta' is the angle bet...

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  6. The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hat...

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  7. If theta is the angle between any two vectors veca and vecb, then |vec...

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  8. Prove that the Iine joining the midpoints of the two sides of a triang...

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  9. Find the projection of vector hati-hatj on the vector hati+hatj

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  10. Show that the line segment joining the midpoints of two 'sides of a t...

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  11. If P=(2,4,7) and Q=(-4,-1,5), then find bar(PQ) and |bar(PQ)|

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  12. i) Compute |hati+hatj+hatk| ii) If veca=2 hati+3 hatj+6 hatk, find th...

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  13. Find a vector in the direction of the vector '-hati+2 hatj+2 hatk' tha...

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  14. Find a unit vector parallel to the sum of vectors veca=2 hati+4 hatj-5...

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  15. Find the condition that the vectors veca=k hati+3 hatj and vecb=4 hati...

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  16. Lẹt 0 be the centre of the regular hexagon ABCDEF. Find the sum of the...

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  17. Show that the diagonals of a quadrilateral bịsect each other if and on...

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  18. Prove that the quadrilatral formed by joining the mid points of the si...

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  19. Find the vector with initial point 'A(6,-2)' and terminal point 'B(4,8...

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  20. The vectors of magnitude a, 2a, 3a meet at a point and their direction...

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