## Lecture - 4 Chapter 10 Vector Algebra

“Believe in yourself! Have faith in your abilities! Without a humble but reasonable confidence in your own powers you cannot be successful or happy.” — **Norman Vincent Peale**

In this video I am discussing about Vector Addition, Triangle Law of Vector Addition, Parallelogram Law of Vector addition, distance formula, sections formula and mid-point formula.

NCERT EXERCISE 10.2 |

**6.** Find the sum of the vectors

\(\vec{a}=\hat{i}-2\hat{j}+\hat{k}\)

\(\vec{b}=-2\hat{i}+4\hat{j}+5\hat{k}\)

\(\vec{c}=\hat{i}-6\hat{j}-7\hat{k}\)

**9.** For given vectors, \(\vec{a}=2\hat{i}-\hat{j}+2\hat{k}\) and \(\vec{b}=-\hat{i}+\hat{j}-\hat{k}\), find a unit vector in the direction of the vector \(\vec{a}+\vec{b}\).

**15.** Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \(\hat{i}+2\hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}+\hat{k}\) respectively, in the ratio 2 : 1

(i) internally

(ii) externally

**16.** Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2).

**17.** Show that the points A, B and C with position vectors \(\vec{a}=3\hat{i}-4\hat{j}-4\hat{k}\), \(\vec{b}=2\hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-3\hat{j}-5\hat{k}\), respectively form the vertices of a right angled triangle.

**18.** In triangle ABC (Fig 10.18), which of the following is not true:

(A) \(\vec{AB}+\vec{BC}+\vec{CA}=\vec{0}\)

(B) \(\vec{AB}+\vec{BC}-\vec{AC}=\vec{0}\)

(C) \(\vec{AB}+\vec{BC}-\vec{AC}=\vec{0}\)

(D) \(\vec{AB}-\vec{CB}+\vec{CA}=\vec{0}\)

**19.** If \(\vec{a} \text{ and } \vec{b}\) are two collinear vectors, then which of the following are incorrect:

(A) \(\vec{b} = \lambda\vec{a}\), for some scalar \(\lambda\)

(B) \(\vec{a} = \pm\vec{b}\),

(C) the respective components of \(\vec{a} \text{ and } \vec{b}\) are not proportional

(D) both the vectors \(\vec{a} \text{ and } \vec{b}\) have same direction, but different magnitudes.