Odisha State Board CHSE Odisha Class 12 Math Notes Chapter 12 Vectors will enable students to study smartly.

## CHSE Odisha 12th Class Math Notes Chapter 12 Vectors

Important formulae:

1. If P = (x_{1}, y_{1}, z_{1}) and Q = (x_{2}, y_{2}, z_{2}) then

P͞Q = (x_{2} – x_{1}) î + (y_{2} – y_{1} ) ĵ + (z_{2} – z_{1}) k̂

where î, ĵ, k̂ are the unit vectors along x-axis, y-axis and z-axis.

2. Magnitude of a vector:

8. Properties of vector product:

(i) Area of a parallelogram whose adjacent sides are represented by the

12. The vector equation of a straight line:

(i) The vector equation of a straight line passing through a point with position vector \(\vec{a}\) and parallel to a vector \(\vec{b}\) is \(\vec{r}=\vec{a}+t \vec{b}\) where t is a parameter.

(ii) The equation ofa striaght line through two points with position vectors \(\vec{a}\) and \(\vec{b}\) is \(\vec{r}=\vec{a}+t(\vec{b}-\vec{a})\).

(iii) Equation of a straight line through a point with position vector \(\vec{a}\) and perpendicualr to two non-parallel \(\vec{b}\) and \(\vec{c}\) is \(\vec{r}=\vec{a}+t(\vec{b} \times \vec{a})\).

13. The vector equation of a plane:

(i) The vector equation of plane through a point \(\vec{a}\) and perpendicular to n̂ is \((\vec{r}-\vec{a}) \cdot \hat{n}\) = 0

(ii) The equation of a plane through a point \(\vec{a}\) and parallel to non-parallel vectors \(\vec{b}\) and \(\vec{c}\) is \(\vec{r}=\vec{a}+t \vec{b}+s \vec{c}\), where t and s are parameters.

(iii) Equation of the plane passing through the points \(\vec{a}, \vec{b}\) and parallel to \(\vec{c}\) is \(\vec{r}=(1-t) \vec{a}+t \vec{b}+s \vec{c}\).

(iv) Equation of the plane through three non collinear points \(\vec{a}, \vec{b}, \vec{c}\) is \(\vec{r}=(1-s-t) \vec{a}+t \vec{b}+s \vec{c}\).