If `vec(p)` is a unit vector and ` ( vec (x) - vec(p)). (vec(x)+vec(p)) = 8 ` , then find ` |vec (x)|`

If vec(p) is a unit and (vec(x) - vec (p)) . (vec(x)+ vec (p)) = 80 then find |vec(x)|

If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then find |vec x|

find |vec x| , if for a unit vector vec a, (vec x- vec a)( vec x + vec a) =12

If vec(a) and vec(b) are two vector such that |vec(a)| = 2, |vec(b)| =3 and vec(a).vec(b) =4 , then find the value of |vec(a)- vec(b)|

Two vectors vec(a) and vec(b) are such that |vec(a)| = 2 , |vec(b)| = 1 and vec(a) . vec(b) = 1 , then find the value of (3 vec(a) - 5 vec(b)).(2 vec(a) + 7vec(b))

If vec(x), vec(y), vec(z) are three vectors, show that the points having positive vectors 7vec(x) - vec(z), vec(x) + 2vec(y) + 3vec(z) and -2vec(x) + 3vec(y) + 5vec(z) are collinear

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

If two vectors vec(a) and vec (b) are such that |vec(a) . vec(b) | = |vec(a) xx vec(b)|, then find the angle the vectors vec(a) and vec (b)

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

Three vectors vec(a),vec(b),vec (c ) are such that vec(a) + vec(b) + vec(c ) = vec(0) , if |vec(a)| = 1 |vec(b)| = 4 and |vec(c )|= 2 , then find the value of mu = (vec(a).vec(b) +vec(b).vec(c ) + vec(c ).vec(a))