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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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VMC MODULES ENGLISH-VECTORS -JEE ADVANCED (ARCHIVE) (TRUE/ FALSE)
  1. about to only mathematics

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  2. Let OACB be a parallelogram with O at the origin and OC a diagonal. Le...

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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. If veca, vecb, vecc and vecd ar distinct vectors such that veca xx v...

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  5. For any two vectors vecu and vecv prove that (1+|vecu|^2)(1+|vecv|^2) ...

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  6. A , B , Ca n dD are any four points in the space, then prove that |...

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  7. about to only mathematics

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  8. vecu, vecv and vecw are three nono-coplanar unit vectors and alpha, be...

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  9. about to only mathematics

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  10. Let vecu and vecv be unit vectors. If vecw is a vector such that vecw+...

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  11. The position vectors of the point A, B, C and D are 3hati-2hatj -hatk,...

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  12. If vecA , vecB and vecC are vectors such that |vecB| = |vecC| prove th...

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  13. If vectors, vecb, vecc and vecd are not coplanar, the prove that vecto...

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  14. If c is a given non - zero scalar, and vecA and vecB are given non- ze...

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  15. about to only mathematics

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  16. Two triangles ABC and PQR are such that the perpendiculars from A to Q...

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  17. Find the position vector of the mid point of the vector joining the p...

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  18. Prove, by vector method or otherwise, that the point of intersectio...

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  19. Let veca, vecb and vecc be non - coplanar unit vectors, equally inclin...

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  20. If vecA,vecB,vecC are three vectors respectively given by 2hati+hatk, ...

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