## Lecture - 3 Chapter 10 Vector Algebra

Whether you are waking up early to go to work, school, or just running some errands, it’s important that you spend a few minutes to sharpen your mind, fill your heart, and think positively so that you can start the day off feeling blessed with a grateful heart.

In this video I am discussing about Direction Cosines and Direction angles.

NCERT EXERCISE 10.2 |

**2.** Write two different vectors having same magnitude.

**3.** Write two different vectors having same direction.

**4.** Find the values of x and y so that the vectors \(2\hat{i}+3\hat{j}\) and \(x\hat{i}+y\hat{j}\) are equal.

**5.** Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).

**7.** Find the unit vector in the direction of the vector \(\vec{a}=\hat{i}+\hat{j}+2\hat{k}\)

**8.** Find the unit vector in the direction of vector \(\vec{PQ}\), where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

**11.** Show that the vectors \(2\hat{i}-3\hat{j}+4\hat{k}\) and \(-4\hat{i}+6\hat{j}-8\hat{k}\) are collinear.

**12.** Find the direction cosines of the vector \(\hat{i}+2\hat{j}+3\hat{k}\)

**13.** Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.

**14.** Show that the vector \(\hat{i}+\hat{j}+\hat{k}\) is equally inclined to the axes OX, OY and OZ.