List of Maths Formulas for 12th Class

List of Maths Formulas for 12th Class

Here is a list of Maths formulas for CBSE class 12.

Vectors and Three Dimensional Geometry Formulas for Class 12

Position Vector	OP−→−=r⃗ =x2+y2+z2−−−−−−−−−−√
Direction Ratios	l=ar,m=mr,n=cr
Vector Addition	PQ→+QR→=PR→
Properties of Vector Addition	CommutativePropertya⃗ +b⃗ =b⃗ +a⃗  AssociativeProperty(a⃗ +b⃗ )c⃗ +=a⃗ +(b⃗ +c⃗ )
Vector Joining Two Points	P1P2−→−−=OP1−→−−OP1−→−
Skew Lines	Cosθ=∣∣∣a1a2+b1b2+c1c2a21+a21+c21√a22+a22+c22√∣∣∣
Equation of a Line	x−x1a=y−y1b=z−z1c

Algebra Formulas For Class 12

Ifa⃗ =xi^+yj^+zk^ then magnitude or length or norm or absolute value of a⃗  is ∣∣a→∣∣=a=x2+y2+z2−−−−−−−−−−√

A vector of unit magnitude is unit vector. If a⃗  is a vector then unit vector of a⃗  is denoted by a^ and a^=a^∣∣a^∣∣ Therefore a^=a^∣∣a^∣∣a^

Important unit vectors are i^,j^,k^, where i^=[1,0,0],j^=[0,1,0],k^=[0,0,1]

If l=cosα,m=cosβ,n=cosγ, then α,β,γ, are called directional angles of the vectorsa→ and cos2α+cos2β+cos2γ=1

In Vector Addition

a⃗ +b⃗ =b⃗ +a⃗

a⃗ +(b⃗ +c⃗ )=(a⃗ +b⃗ )+c⃗

k(a⃗ +b⃗ )=ka⃗ +kb⃗

a⃗ +0⃗ =0⃗ +a⃗ , therefore 0⃗  is the additive identity in vector addition.

a⃗ +(−a⃗ )=−a⃗ +a⃗ =0⃗ , therefore a⃗   is the inverse in vector addition.

Trigonometry Class 12 Formulas

Definition

θ=sin−1(x)isequivalenttox=sinθ

θ=cos−1(x)isequivalenttox=cosθ

θ=tan−1(x)isequivalenttox=tanθ

Inverse Properties

sin(sin−1(x))=x

cos(cos−1(x))=x

tan(tan−1(x))=x

sin−1(sin(θ))=θ

cos−1(cos(θ))=θ

tan−1(tan(θ))=θ

Double Angle and Half Angle Formulas

sin(2x)=2sinxcosx

cos(2x)=cos2x–sin2x

tan(2x)=2tanx1–tan2x

sinx2=±1–cosx2−−−−−√

cosx2=±1+cosx2−−−−−√

tanx2=1−cosxsinx=sinx1–cosx