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If two side of a triangle are hat i+...

If two side of a triangle are ` hat i+2 hat ja n d hat i+ hat k` , then find the length of the third side.

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Given sides of the triangle are `veca=hati+2hatj and vecb=hati+hatk`.
If vector along the third side is `vecc`, then we must have `veca+vecb+vecc=0`. Then
`" "vecc=-(hati+2hatj)-(hati+hatk)=-2hati-2hatj-hatk`
Therefore, the length of the third side `|vecc|` is `sqrt((-2)^(2)+(-2)^(2)+(-1)^(2)) =3`.
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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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  3. A vector a has components a1,a2,a3 in a right handed rectangular cart...

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

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

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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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  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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  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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