If ` vec An d vec B` are two vectors and `k` any scalar quantity greater than zero, then prove that `| vec A+ vec B|^2lt=(1+k)| vec A|^2+(1+1/k)| vec B|^2dot`

If vec a and vec b are two vectors such that vec a + vec b is perpendicular to vec a - vec b ,then prove that |vec a| = |vec b| .

If vec aa n d vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec bdot

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector, ) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

For any vectors vec a vec b , show that |vec a + vec b| le |vec a| + |vec b| .

If vec a and vec b are orthogonal vectors, prove that (vec a + vec b)^(2) = (vec a - vec b)^(2) .

For any three vectors veca, vec b, vec c prove that (vec a + vec b)+ vec c = vec a + (vec b + vec c)

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

If vec a , a n d vec b are unit vectors , then find the greatest value of | vec a+ vec b|+| vec a- vec b|dot