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 vec(a) and vec(b) , prove 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||vec b| .

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

vec(a) and vec(b) are any two vectors. Prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)|

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

If vec(a), vec(b) " and " vec(c) are unit vectors satisfying abs(vec(a)-vec(b))^(2)+abs(vec(b)-vec(c))^(2)+abs(vec(c)-vec(a))^(2)=9, " then " abs(2vec(a)+5vec(b)+5vec(c)) is -

If abs(vec(a)+vec(b))=abs(vec(a)-vec(b)) , then show that vec(a) and vec(b) are perpendicular to each other.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .