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If 2 vec A C = 3 vec C B , then prove th...

If 2` vec A C` = 3` vec C B` , then prove that 2` vec O A` =3` vec C B` then prove that 2` vec O A` + 3` vec O B` =5` vec O C` where `O` is the origin.

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`2vec(AC)=3vec(CB)` or `2(vec(OC)-vec(OA))=3(vec(OB)-vec(OC))`
or `" "2vec(OA)+3vec(OB)=5vec(OC)`
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Statement 1:Let A( vec a),B( vec b)a n dC( vec c) be three points such that vec a=2 hat i+ hat k , vec b=3 hat i- hat j+3 hat ka n d vec c=- hat i+7 hat j-5 hat kdot Then O A B C is a tetrahedron. Statement 2: Let A( vec a),B( vec b)a n dC( vec c) be three points such that vectors vec a , vec ba n d vec c are non-coplanar. Then O A B C is a tetrahedron where O is the origin.

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CENGAGE-INTRODUCTION TO VECTORS -JEE Previous Year
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  2. Find the values of lambda such that x ,y ,z!=(0,0,0)a n d( hat i+ hat ...

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

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  10. about to only mathematics

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  11. If |{:(a,,a^(2),,1+a^(3)),(b,,b^(2),,1+b^(3)),(c,,c^(2),,1+c^(3)):}|=0...

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  12. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

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  13. The points with position vectors veca + vecb, veca-vecb and veca +k ve...

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  14. The points with position vectors 60hati+3hatj,40hati-8hatj,ahati-52hat...

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  15. Let a, b and c be distinct non-negative numbers. If vectos a hati +a h...

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  16. Let veca =hati -hatk, vecb = xhati+ hatj + (1-x)hatk and vecc =y hati ...

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  17. about to only mathematics

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

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  19. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahatj...

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  20. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

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  21. Suppose that vec p,vecqand vecr are three non- coplaner in R^(3) ,Let...

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