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Let vec A(t) = f1(t) hat i + f2(t) hat ...

Let `vec A(t) = f_1(t) hat i + f_2(t) hat j and vec B(t) = g(t)hat i+g_2(t) hat j,t in [0,1],f_1,f_2,g_1, g_2` are continuous functions. If `vec A(t) and vec B(t)` are non-zero vectors for all `t and vec A(0) = 2hat i + 3hat j,vec A(1) = 6hat i + 2hat j, vec B(0) = 3hat i + 2hat i and vec B(1) = 2hat i + 6hat
j` Then,show that `vec A(t) and vec B(t)` are parallel for some `t`.

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Prove that the four points 6 hat i-7 hat j ,16 hat i-19 hat j-4 hat k ...

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  2. Show, by vector methods, that the angularbisectors of a triangle are c...

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  3. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

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  4. Find the least positive integral value of x for which the angle betwee...

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  5. If vectors vec a= hat i+2 hat j- hat k , vec b=2 hat i- hat j+ hat k ...

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  6. Find the values of lambda such that x ,y ,z!=(0,0,0) and ( hat i+ hat ...

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  7. A vector has component A1, A2a n dA3 in a right -handed rectangular Ca...

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  8. The position vectors of the point A ,B ,C and D are 3 hat i-2 hat j- h...

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  9. Let O A C B be a parallelogram with O at the origin andO C a diagonal....

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  10. In a triangle A B C ,Da n dE are points on B Ca n dA C , respectivley,...

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  11. Prove by vector method that the line segment joining the mid-points...

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  12. If the resultant of two forces is equal in magnitude to one of the ...

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  13. The axes of coordinates are rotated about the z-axis through an angle ...

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  14. Prove that the sum of three vectors determined by the medians of a ...

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  15. If two side of a triangle are hat i+2 hat j and hat i+ hat k , then...

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  16. If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 ha...

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  17. Find the resultant of vectors vec a= hat i- hat j+2 hat k and vec b...

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  18. Check whether the three vectors 2 hat i+2 hat j+3 hat k ,-3 hat i+3...

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  19. The midpoint of two opposite sides of a quadrilateral and the midpo...

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  20. Prove that the lines joining the vertices of a tetrahedron to the ce...

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