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Prove that the four points 4 hat i +5 ha...

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.

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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 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 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.

Show that the points A(2 hat i - hat j + hat k) , B(hat i - 3 hat j- 5 hat k ) and C(3 hat i - 4 hat j- 4 hat k) are the vertices of a right angled triangle.

Show that the vectors 2 hat i -3 hat j +4 hat k and -4 hat i +6 hat j -8 hat k are collinear.

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).

Write the value of: (hat i . (hat j xx hat k) + hat j (hat k xx hat i ) + hat k . (hat j xx hat i)

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.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find λ if vectors vec a = hat i +λ hat j +hat k, vec b= 2hat i -hat ...

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  2. Find the value of scalar λ if the vectors vec a =2 hat i +hat j +hat ...

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

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  4. Integrate the following int (2x+6)dx/(x^2+6x+49)

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  5. Show that the four points having position vectors 6 hat i-7 hat j, 16 ...

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  6. Integrate the following int xlog3xdx

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  7. If vec a =3 hat i -hat j +hat k, vec b= hat i +3hat j - hat k and ve...

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  8. Integrate the following int dx/(x^2+10x+9)

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  9. If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b...

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  10. For any vector vec a, prove that hat i xx (vec a xx hat i)+ hat j xx (...

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  11. If a,b and c are three non-zero vectors such that a*(bxxc)=0 and b and...

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  12. Integrate the following int xcos5xdx

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  13. What is the magnitude of a unit vector ?

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  14. If vec a = x hat i +2 hat j - z hat k and vec b= 3 hat i- y hat j+hat ...

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  15. Does |quad vec a|= |quad vec b| imply vec a= vec b?

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  16. State whether the vectors hat i, hat j and hat k are coplanar or non-c...

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  17. Integrate the following int dx/(1-secx)

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  18. What is the cosine of the angle which the vector sqrt2 hat i+ hat j +h...

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  19. Find p if the vectors 2 hat i +3 hat j + 6 hat k and p hat i+2 hat j-...

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  20. Find λ if the vector λ (hat i+ hat j+ hat k) is a unit vector.

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