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If vec(a)=x(1)hat(i)+y(1)hat(j) & vec(b)...

If `vec(a)=x_(1)hat(i)+y_(1)hat(j)` & `vec(b)=x_(2)hat(i)+y_(2)hat(j)`. The condition that would make `vec(a)` & `vec(b)` parallel to each other is _____________?

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The correct Answer is:
`x_(1)y_(2)=x_(2)y_(1)`
Parallel vectors make equal angle from x-axis.
`tan theta =(y_(1))/(x_(1))=(y_(1))/(x_(2)) rArr y_(1)x_(2) =y_(2)x_(1)`
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BANSAL-UNIT DIMENSION, VECTOR & BASIC MATHS-EXERCISE - 3 (Miscellaneous Exercise)
  1. The two vectors A=2hat(i)+hat(j)+3hat(k) and B=7hat(i)-5hat(j)-3hat(k...

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  2. A plumber steps out of his truck, walks 60m east and 35m south and the...

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  3. Find the resultant of the three vectors shown in figure (2W1). .

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  4. If vec(a)=x(1)hat(i)+y(1)hat(j) & vec(b)=x(2)hat(i)+y(2)hat(j). The co...

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  5. A bird moves from point (1, -2) to (4, 2) . If the speed of the bird i...

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  6. vec(A)+vec(B)=2hat(i) and vec(A)- vec(B)=4hat(j) then angle between v...

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  7. Given the vectors vec(A)=2hat(i)+3hat(j)-hat(k) vec(B)=3hat(i)-2h...

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  8. A body constrained to move in y direction is subjected to a force give...

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  9. If the resultant of two forces of magnitudes P and Q acting at a point...

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  10. If the resultant of two forces of magnitudes p and 2p is perpendicular...

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  11. Given that vec(a)=vec(i)+vec(j) +vec(k), vec(b)=vec(i)-vec(j)+vec(k), ...

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  12. |vec(a)|=2,|vec(b)|=3,|vec(c)|=6 . Angle between vec(a) and vec(b),vec...

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  13. The magnitude of the vector hat(i)+xhat(j)+3hat(k) is half of the magn...

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  14. The resultant of two forces , one double the other in magnitude is pe...

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  15. Two vectors vec(A) & vec(B) are given such that angle between (vec(A)+...

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  16. Find the magnitude of the unknown forces if sum of all forces is zero.

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  17. Three boys are pulling a heavy trolley by means of 3 ropes. The boy in...

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  18. A particle is displaced from A=(2,2,4) to B=(5, -3,-1) . A constant fo...

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  19. A force vec(F)=3hat(i)+chat(j) +2hat(k) acting on a particle causes a ...

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  20. A mosquito net over a 7ftxx4 ft bed is 3 fthigh. The net has a hole at...

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