A Note In Example , one may note that although but the points A, B and C do not form the vertices of a triangle. EXERCISE . . Find the angle between two vectors with magnitudes and , respectively having .
Find the angle between the vectors . Find the projection of the vector ˆ on the vector ˆ . Find the projection of the vector on the vector . Show that each of the given three vectors is a unit vector: ( ), ( ), ( ) Also, show that they are mutually perpendicular to each other.
. Find , if . Evaluate the product . Find the magnitude of two vectors , having the same magnitude and such that the angle between them is o and their scalar product is .
Find , if for a unit vector , . If are such that is perpendicular to , then find the value of λ . . Show that is perpendicular to , for any two nonzero vectors .
If , then what can be concluded about the vector ? . If are unit vectors such that , find the value of . If either vector .
But the converse need not be true. Justify your answer with an example. . If the vertices A, B, C of a triangle ABC are ( , , ), (– , , ), ( , , ), respectively, then find ∠ ABC.
[ ∠ ABC is the angle between the vectors ]. . Show that the points A( , , ), B( , , ) and C( , , – ) are collinear. .
Show that the vectors and k i form the vertices of a right angled triangle. . If is a nonzero vector of magnitude ‘ a ’ and λ a nonzero scalar, then λ is unit vector if (A) λ = (B) λ = – (C) a = | λ | (D) a = /| λ | . .
Vector (or cross) product of two vectors In Section . , we