Vector Algebra Formulas
We use various formulas in Vector Algebra to solve various types of complex problems. These formulas are very helpful in understanding and solving vector algebra problems. The important vector algebra formulas are,
- (ai + bj + ck) + (pi + qj + rk) = (a+p)i + (b+q)j + (c+r)k
- (ai + bj + ck) – (pi + qj + rk) = (a-p)i + (b-q)j + (c-r)k
- (ai + bj + ck) . (pi + qj + rk) = (a.p)i + (b.q)j + (c.r)k
If vector A = ai + bj + ck and vector B = pi + qj + rk, then
- A × B = (br – cq)i + (ar – cp)j + (aq – bp)k
The angle between two vectors is given as,
- θ = cos-1 (a·b/|a||b|)
Associative Property of Multiplication
- A.B = B.A
- A × B ≠ B × A
- A × B = -B × A
Other Properties
- i.i = j.j = k.k = 1
- i.j = j.k = k.i = 0
- i×j = k
- j×k = i
- k×i = j
Vector Algebra
Vectors algebra is the branch of algebra that involves operations on vectors. Vectors are quantities that have both magnitude and direction so normal operations are not performed on the vectors. We can add, subtract, and multiply vector quantities using special vector algebra rules. Vectors can be easily represented in 2-D or 3-D spaces. Vector algebra has various applications it is used in solving various problems in mathematics and physics, engineering, and various other fields.
In this article, we will learn about vector algebra, operations in vector algebra, types of vectors, and others in detail.