Vector Algebra Examples
Example 1: Find the dot product of vectors P(a, b, c) and Q(p, q, r).
Solution:
We know that dot product of the vector is calculated by the formula,
P.Q = P1Q1+P2Q2+……….PnQn
Thus,
P.Q = a.p + b.q + c.r
The dot product of vector P and vector Q is ap + bq + cr
Example 2: Find the dot product of vectors P(1, 3, -5) and Q(7, -6, -2).
Solution:
We know that dot product of the vector is calculated by the formula,
P.Q = P1Q1+P2Q2+……….PnQn
Thus,
P.Q = 1.7 + 3.(-6) + (-5).(-2)
⇒ P.Q = 7 – 18 + 10
⇒ P.Q = 17 – 18
⇒ P.Q = -1The dot product of vector P and vector Q is -1
Example 3: Let’s say two vectors are defined as and . Find,
Solution:
Given,
….(1)
….(2)
Now, let’s calcualte +
Example 4: Find the magnitude of the vector A = 2i – 5j + 4k, using vector algebra.
Solution:
Given Vector,
Vector A = 2i – 5j + 4k
We know that magnitude of the vector A is |A| i.e.
|A| = √ (a2+b2+c2)
⇒ |A| = √ (22+(-5)2+42)
⇒ |A| = √(4 + 25 + 16)
⇒ |A| = √(45) = 3√(5)
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.