# Lecture 4 Vector Algebra Class 12 Maths

## 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.