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For any two vectors ` vec a\ a n d\ vec b` prove that `| vec axx vec b|^2=| (veca. veca , veca. vecb),(vecb.veca ,vecb.vecb)|`

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Statement 1: If V is the volume of a parallelopiped having three coterminous edges as veca, vecb , and vecc , then the volume of the parallelopiped having three coterminous edges as vec(alpha)=(veca.veca)veca+(veca.vecb)vecb+(veca.vecc)vecc vec(beta)=(veca.vecb)veca+(vecb.vecb)vecb+(vecb.vecc)vecc vec(gamma)=(veca.vecc)veca+(vecb.vecc)vecb+(vecc.vecc)vecc is V^(3) Statement 2: For any three vectors veca, vecb, vecc |(veca.veca, veca.vecb, veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc)|=[(veca,vecb, vecc)]^(3)

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In a triangle PQR, "let: aveca= vecQR= vecb= vecRP and vec c= vecPQ . , If |veca|=3, |vecb|=4 and (veca. (vec c. vecb))/(vec. (veca- vecb))=(|veca|)/(|veca|+|vecb|) then the value of |vecaxx vecb|^(2) is _____

RD SHARMA-VECTOR OR CROSS PRODUCT -Solved Examples And Exercises
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  11. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  12. If either -> a= ->0 and -> b= ->0 then -> axx -> b= ->0 . Is ...

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  13. If vec a=a1 hat i+a2 hat j+a3 hat k ,\ vec b=b1 hat i+b2 hat j+b3 ha...

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  14. Using vectors, find the area of the triangle with vertices A(1,1,2),\ ...

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  15. Find all vectors of magnitude 10sqrt(3) that are perpendicular to the ...

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  16. Define vector product of two vectors.

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  17. Write the value ( hat ixx hat j)dot hat k+ hat idot hat jdot

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  18. Write the value of hat idot( hat jxx hat k)+ hat jdot( hat kxx hat i)...

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  19. Write the value of hat idot( hat jxx hat k)+ hat jdot( hat kxx hat i)...

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  20. Write the value of hat ixx( hat j+ hat k)+ hat jxx( hat k+ hat i)+ ha...

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