CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

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 = (x1, y1, z1) and Q = (x2, y2, z2) then
P͞Q = (x2 – x1) î + (y2 – y1 ) ĵ + (z2 – z1) k̂
where î, ĵ, k̂ are the unit vectors along x-axis, y-axis and z-axis.

2. Magnitude of a vector:
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 1
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 2

CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

8. Properties of vector product:
(i) Area of a parallelogram whose adjacent sides are represented by the
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 3
CHSE Odisha Class 12 Math Notes Chapter 12 Vectors 4
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 \(\vec{r}=\vec{a}+t(\vec{b} \times \vec{a})\).

CHSE Odisha Class 12 Math Notes Chapter 12 Vectors

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 \(\vec{r}=(1-s-t) \vec{a}+t \vec{b}+s \vec{c}\).

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