F3E) 3 B) Show that for two vectors and 6 always. a + b

For any two vectors -> a and -> b we always have | -> adot -> b|lt=| -> a|| -> b| (Cauchy-Schwartz inequality).

For any two vectors -> a and -> b we always have | -> adot -> b|lt=| -> a|| -> b| (Cauchy-Schwartz inequality).

Show that the resultant of two vectors vec(A) and vec(B) always lies between A + B and A - B

Show that the two vectors vec(A) and vec(B) are parallel , where vec(A) = hat(i) + 2 hat(j) + hat(k) and vec(B) = 3 hat(i) + 6 hat(j) + 3 hat(k)

For any two vectors vec a and vec b, we always have |vec a+ vec b|<=|vec a|+|vec b|

If the resultant of two vectors having magnitudes of 6 and 3 is 9 then the dot product of two vectors is (A) 6 (B) 3 (C) "9 (D) 18

The position vector of two points A and B are 6vec(a) + 2vec(b) and vec(a) - vec(b) . If a point C divides AB in the ratio 3:2 then shown that the position vector of C is 3vec(a) - vec(b) .

Show that | -> a| -> b+| -> b| -> a is perpendicular to | -> a| -> b-| -> b| -> a , for any two nonzero vectors -> a and -> b .

Show that | -> a| -> b+| -> b| -> a is perpendicular to | -> a| -> b-| -> b| -> a , for any two nonzero vectors -> a and -> b .