If `| vec a X vec b|^2+| vec adot vec b|^2=400` and `| vec a|=5,` then write the value of `| vec b|dot`

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

If |vec(a) xx vec(b)|^(2) + |vec(a) .vec(b)|^(2) = 400 and |vec(a)| = 5 , then write the value of |vec(b)| .

If | vec axx vec b|^2=( vec adot vec b)^2=144\ a n d\ | vec a|=4 , find vec bdot

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

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

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

For any two vectors vec a and vec b , prove that: | vec a+ vec b|^2=| vec a|^2+| vec b|^2+2 vec adot vec b , | vec a- vec b|^2=| vec a|^2+| vec b|^2-2 vec adot vec b , | vec a+ vec b|^2+| vec a- vec b|^2=2(| vec a|^2+| vec b|^2) and | vec a+ vec b|^2=| vec a- vec b|^2 iff vec a_|_ vec bdot Interpret the result geometrically.

If vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c= vec0, then write the value of vec a . vec b+ vec b . vec c+ vec c . vec a

If two vectors vec a\ a n d\ vec b are such that | vec a|=2,\ | vec b|=1\ a n d\ vec adot vec b=1, then find rthe value of (3 vec a-5 vec b)dot'(2 vec a+7 vec b)'dot

If vec aa n d 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]dot