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Show that the four points with position vectors `4hati+8 hat j +12hat k, 2 hat i+4hat j +6hat k, 3 hat i +5hat j +4hatk and 5hat i+8hat j+5hatk` are coplanar.

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Prove that the points whose position vectors are 6 hat i - 7 hat j, 16 hat i -29 hat j -4 hat k , 3 hat j -6 hat k and 2 hat i+5 hat j +10 hat k are coplanar.

Show that the four points having position vectors 6 hat i-7 hat j, 16 hat i-19 hat j -4hat k, 3 hat j-6 hat k, 2 hat i+5 hat j +10 hat k are not coplanar.

Find λ if the vectors hat i-hat j+ hat k, 3 hat i+ hat j+ 2 hat k and hat i+ λ hat j- 3 hat k are coplanar.

Prove that the vectors 2 hat i- hat j+ hat k , hat i- 3 hat j- 5 hat k and 3 hat i- 4 hat j- 4 hat k are coplanar.

Prove that the points whose position vectors are hat i - hat j+ hat k , 2 hat i+ 3 hat j+ hat k , hat i+ 2 hat j+ 3 hat k , -2 hat j+ 3 hat k lie in the same plane.

Show that the points A,B and C whose position vectors are repectively 2 hat i+ hat j- hat k , 3 hat i- 2 hat j+ hat k and hat i+ 4 hat j- 3 hat k are collinear.

Prove that the four points 4 hat i +5 hat j +hat k, -(hat j+hat k) ,3 hat i+ 9 hat j +4hat k and 4(-hat i+hat j + hat k) are coplanar.

Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + 3hat j- 4hat k and vec c =hat i - 3 hat j+5 hat k are coplanar.

Show that the point A,B,C and D whose position vectors are respectively 2 hat i+ 4 hat j+ 2 hat k , hat i+ 2 hat j+ hat k , 3 hat i+ hat j- 3 hat k and 4 hat i+3 hat j - 2 hat k are the vertices of a paralleogram (use vector method).

Show that the vectors vec a= 10 hat i -12 hat j -4 hat k, vec b=-16 hat i +22 hat j- 2 hat k and vec c = 2hat i -8 hat j +16hat k are coplanar.

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. Let vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c1 hat i + ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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