Find `| -> a|` and `| -> b|` , if `( -> a+ -> b)dot( -> a- -> b)=8` and `| -> a|=8| -> b|`

Let's resolve into factor:- 3(a + b)^2 - 2a - 2b - 8

Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

If | vec a|=5,| vec a- vec b|=8 and | vec a+ vec b|=10 , then find | vec b|dot

Find the values of a and b for which the equations 5x+8y=7 and (a+b)x+(a-b)y=(2a+b+1) will have infinitely many sets of solution.

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| d. none of these

If ( vec axx vec b)^2+( vec a.vec b)^2=144 and | vec a|=4, then find the value of | vec b|dot

In an acute triangle A B C , if the coordinates of orthocentre H are (4,b) , of centroid G are (b ,2b-8) and of circumcenter S are (-4,8) , then b cannot be (a) 4 (b) 8 (c) 12 (d) -12

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

Find q and r for the following pairs of positive integers a and b, satisfying a = bq + r. a = 80 , b = 8

If | vec a|=2| vec b|=5 and | vec axx vec b|=8, then find the value of vec a . vec bdot