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

Prove that `(veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2)`, if and only if `veca,vecb` are perpendicular , given `vecanevec0,vecbnevec0`.
Choose the correct answer in Exercises 16 to 19.

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NCERT GUJARATI-VECTOR ALGEBRA-Miscellaneous Exercise on chapter 10
  1. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  2. Find the scalar components and magnitude of the vector joining the poi...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

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  4. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  5. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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  6. A vector has magnitude 5 units. It is parallel to the resultant vector...

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  7. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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  8. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

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  9. Find the position vector of a point R which divides the line joining t...

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  10. The two adjacent sides of a parallelogram are 2hati-4hatj+5kandhati-2h...

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  11. Show that the direction cosines of a vector equally inclined to the ax...

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  12. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatkandvecc=2hati-hatj+4ha...

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  13. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  14. Prove that (veca+vecb)*(veca+vecb)=|veca|^(2)+|vecb|^(2), if and only...

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  15. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

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  16. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

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  17. The value of hati.(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) is

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  18. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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