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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 j + 6hat j` Then,show that `vec A(t) and vec B(t)` are parallel for some `t`.

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MOTION-VECTOR -EXERCISE - 4 ( LEVEL-II)
  1. If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+|vecb-vec|^2+...

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  2. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

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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 and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  5. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  6. The value of a so that the volume of the paralelopiped formed by hati+...

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  7. A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+h...

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  8. If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vec...

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  9. If veca,vecb,vecc,vecd are four distinct vectors satisfying the condit...

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  10. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

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  11. Let vecA be a vector parallel to the of intersection of planes P1 and ...

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  12. The number of distinct values of lamda, for which the vectors -lamda^(...

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  13. Let veca, vecb ,vecc be unit vetors such that veca + vecb + vecc = ve...

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  14. Assertion: vec(PQ)xx(vec(RS)+vec(ST))!=0, Reason : vec(PQ)xxvec(RS)=ve...

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  15. The edges of a parallelopiped are of unit length and are parallel to n...

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  16. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  17. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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  18. Let P, Q, R and S be the points on the plane with position vectors -2h...

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  19. If veca and vecb are vectors in space given by veca=(hati-23hatj)/(sqr...

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  20. Let veca=hati + hatj +hatk,vecb=hati- hatj + hatk and vecc= hati-hatj...

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