Solution Let is a scalar, i.e., Now ( ) ( −λ + λ Now, since β is to be perpendicular to α r , we should have . i.e., ( ) ( −λ − + λ = or λ = Therefore = Miscellaneous Exercise on Chapter . Write down a unit vector in XY-plane, making an angle of ° with the positive direction of x -axis. .
Find the scalar components and magnitude of the vector joining the points P( x , y , z ) and Q( x , y , z ). . A girl walks km towards west, then she walks km in a direction ° east of north and stops. Determine the girl’s displacement from her initial point of departure.
. If , then is it true that ? Justify your answer. .
Find the value of x for which x i is a unit vector. . Find a vector of magnitude units, and parallel to the resultant of the vectors . If , find a unit vector parallel to the vector .
Show that the points A( , – , – ), B( , , – ) and C( , , ) are collinear, and find the ratio in which B divides AC. . Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are externally in the ratio : . Also, show that P is the mid point of the line segment RQ.
. The two adjacent sides of a parallelogram are and Find the unit vector parallel to its diagonal. Also, find its area. .
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are ± . Let . Find a vector which is perpendicular to both and , and . The scalar product of the vector with a unit vector along the sum of vectors λ + is equal to one.