For the vectors `vec(a) " and " vec(b)` show that
(i) `abs(vec(a)+vec(b)) le abs(vec(a))+abs(vec(b)) " (ii) " abs(abs(vec(a))-abs(vec(b))) le abs(vec(a)-vec(b))`

For any two vectors vec(a) and vec(b) , show that | vec (a).vec(b)| le |vec(a)||vec(b)|

For any two vectors veca and vec b show that |vec a.vec b|le |vec a|.|vecb|

If vec(a)=vec(OA) " and " vec(b)=vec(AB), " then " vec(a)+vec(b) is -

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-

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(a)=2hat(i)+5hat(j)-2hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k) , then find (i) vec(a)+vec(b) " and " 2vec(a)-3vec(b) " " (ii)abs(vec(a)+vec(b)) " and " abs(vec(a)-2vec(b)) (iii) a unit vector in the direction (vec(a)+vec(b)) (iv) vector and scalar components of the vector (2vec(a)-3vec(b)) along the coordinate axes.

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

Show that the vector vec(a) is perpendicular to the vector vec(b) - (vec(a).vec(b))/(|vec(a)|^(2))vec(a)

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

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