Question

Let u,vu,v and ww be vectors such that u+v+wu+v+w. If |u|=3,|v|=4|u|=3,|v|=4 and ||w|=5||w|=5. Then the value of u.v+v.w+w.uu.v+v.w+w.u is

• A. $47$
• B. $-25$
• C. $0$
• D. $25$

Answer 1

The correct option is B $-25$

Taking dot product with u,v and w respectively in $u+v+w=0$ we get

$u.u+u.v+u.w=0$

$v.u+v.v=v.w=0$

$w.v+w.v+w.w=0$

Adding the above equation we get

$2(u.u+u.w+v.w)=-({\left|u\right|}^2+{\left|v\right|}^2+{\left|w\right|}^2)$

$=-(9+16+25)$

$=-50$

Hence $u.v+u.w+v.w=-25$

Answer : -25