Home
Class 12
MATHS
(Cauchy-Schawarz inequality) For any two...

(Cauchy-Schawarz inequality) For any two vectors ` vec a\ a n d\ vec b` prove that `( vec adot vec b)^2lt=| vec a|^2| vec b|^2` and hence show that `(a_1b_2+a_2b_2+a_3b_3)^2lt=(a1 2+a2 2+a3 2)(b1 2+b2 2+b3 2)dot`

Promotional Banner

Similar Questions

Explore conceptually related problems

For any two vectors vec a and vec b prove that ( veca dot vecb)^2le| vec a|^2| vec b|^2 and hence show that (a_1b_2+a_2b_2+a_3b_3)^2lt=(a_1^2+a_2^2+a_3^2)(b_1^2+b_2^2+b_3^2)

For any vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

For any two vectors vec a and vec b , prove that (vec a xx vec b )^2= |vec a |^2 |vec b|^2 -(vec a. vec b)^2

If | vec a|= a\ a n d\ | vec b|=b, prove that ( vec a/(a^2)- vec b/(b^2))^2=(( vec a- vec b)/(a b))^2

For any two vectors vec aa n d vec b , show that (1+| vec a|^2)(1+| vec b|^2)={"("1+ vec a.vec b")"^2| vec a+ vec b+( vec axx vec b)|^2

For any two non zero vectors write the value of (| vec a+ vec b|^2+| vec a- vec b|^2)/(| vec a|^2+ | vec b"|^2)

Find | vec a|a n d| vec b|,if( vec a - vec b)dot ( vec a+ vec b) =27 and | vec a|=2| vec b|dot

Find | vec a- vec b|, if two vector vec a and vec b are such that | vec a|=2,| vec b|=3 and vec adot vec b=4 .

If vec a , vec b , vec c are unit vector, prove that | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2lt=9.

If | vec a|=a and | vec b|=b , prove that ( vec a/(a^2)- vec b/(b^2))^2 = (( vec a- vec b)/(a b))^2 .