Chapter 10
Compute the magnitude of the following vectors: = ˆ ˆ ;i j k+ + = ˆˆ ˆ2 7 3 ;i j k− − = 1 1 1 ˆˆ ˆ 3 3 3 i j k+ −
Write two different vectors having same magnitude.
Write two different vectors having same direction.
Find the values of x and y so that the vectors ˆ ˆ ˆ ˆ2 3 and i j xi yj+ + are equal.
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (- 5, 7).
Find the sum of the vectors = ˆˆ ˆ 2 ,i j k− + = ˆˆ ˆ2 4 5i j k− + + and = ˆˆ ˆ 6 - 7c i j k= − .
Find the unit vector in the direction of the vector = ˆˆ ˆ 2a i j k= + + .
Find the unit vector in the direction of vector , where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
For given vectors, = ˆˆ ˆ2 2i j k− + and = ˆˆ ˆi j k− + − , find the unit vector in the direction of the vector .
Find a vector in the direction of vector ˆˆ ˆ5 2i j k− + which has magnitude 8 units.
Show that the vectors ˆ ˆˆ ˆ ˆ ˆ2 3 4 and 4 6 8i j k i j k− + − + − are collinear.
Find the direction cosines of the vector ˆˆ ˆ 2 3i j k+ + .
Find the direction cosines of the vector joining the points A (1, 2, -3) and B (-1, -2, 1), directed from A to B.
Show that the vector ˆˆ ˆi j k+ + is equally inclined to the axes OX, OY and OZ.
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are ˆ ˆˆ ˆ ˆ ˆ2 and -i j k i j k+ − + + respectively, in the ratio 2 : 1 (i) internally (ii) externally
Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, -2).
Show that the points A, B and C with position vectors, = ˆˆ ˆ3 4 4 ,i j k− − = ˆˆ ˆ2i j k− + and = ˆˆ ˆ 3 5i j k− − , respectively form the vertices of a right angled triangle.
In triangle ABC (Fig 10.18), which of the following is not true: (A) (B) (C) (D)
If are two collinear vectors, then which of the following are incorrect: (A) (B) (C) the respective components of are not proportional (D) both the vectors have same direction, but different magnitudes.