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

Let `vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c_1 hat i + c_2 hat j +c_3 hat k`. Then (a) if `c_1 = 1 and c_2 = 2`, find `c_3`, which makes `vec a,vec b and vec c` coplanar.

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Let vec a= hat i+ hat j+ hat k and vec b = hat i and vec c=c_1 hat i + c_2 hat j +c_3 hat k . Then if c_2 =-1 and c_3 = 1 , show that no value of c_1 , can makes vec a,vec b and vec c coplanar.

If vec a = 2hat i - hat j+ 3hat k and vec b =4 hat i+ hat j - 3 hat k , find vec a + vec b .

If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k , find vec a - 2vec b .

If vec a = 2hat i -3 hat j+ 3hat k and vec b =3 hat i- hat j - 4 hat k , find vec a + vec b .

If vec a = 5hat i - hat j- 2hat k and vec b =5 hat i+ hat j - 2 hat k , find 3vec a - vec b .

If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k , find 2 vec a- vec b .

If vec a = hat i + hat j+ 2hat k and vec b =2 hat i+ hat j - 2 hat k , find vec a + vec b .

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If vec a=4 hat i+3 hat j+hat k and vec b=hat i-2 hat k , find | vec a *vec b| .

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Show that the vectors vec a= hat i- 2hat j+ 3hat k, vec b,= -2hat i + ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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