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Find 'x' such that the four points : A(3...

Find `'x'` such that the four points : A(3,2,1),B(4,x,5),C(4,2,-2) and D(6,5,-1) are coplanar.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Let vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c1 hat i + ...

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  2. Show that the four points with position vectors 4hati+8 hat j +12hat k...

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  3. Find 'x' such that the four points : A(3,2,1),B(4,x,5),C(4,2,-2) and D...

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  4. If a,b and c are coplanar show "[a+b b+c c+a]" are coplanar.

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  5. Write down a unit vector in XY-plane, making an angle of 30^o with the...

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

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

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  8. If vec a= vec b + vec c then is it true that |vec a|= |vec b|+ |vec c|...

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  9. Find the value of x for which x (hat i +hat j +hat k) is a unit vector...

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  10. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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  11. If vec a= hat i+hat j+hat k , vec b = 2 hat i- hat j+3 hat k and vec c...

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  12. Show that the points A (1, - 2, - 8), B (5, 0,- 2) and C (11, 3, 7) ar...

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

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  14. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hatk a...

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

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  16. Let a=hat(i)+4hat(j)+2hat(k), b=3hat(i)-2hat(j)+7hat(k) and c=2hat(i)-...

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  17. The scalar product of the vectorhat i+hat j+ hatk with a unit vector a...

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  18. If vec a, vec b ,vec c are mutually perpendicular vectors of equal ma...

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  19. Prove that (vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and ...

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  20. If θ is the angle between two vectors vec a and vec b, then vec a*vec ...

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