Definition Of Length Of A Vector

Length of a Vector is nothing but the magnitude of a vector. The length of a vector v is given by| V |.

More About Length of a Vector

Length or magnitude of a vector can never be negative.
In two-dimensional vector space, we can find the length of a vector by using the Pythagorean rule.
In two-dimensional vector space, the length of the vector v = is given as 
In three-dimensional vector space, the length of the vector v = is given as .

Video Examples: Maths - Measurement Length

Example of Length of a Vector

Length of a vector v = <15, 20=""> =.
Length of a vector v = <3, 4,="" 6=""> =

Solved Example on Length of a Vector

Ques: Find the length of the vector  . [Given b = 40 and c = 9.]

Choices:

A. 40
B. 41
C. 45
D. 51
Correct Answer: B

Solution:

Step 1: In â–³OPM, OP =  [Pythagorean Theorem.]
Step 2: OP = = 41 [Substitute and simplify.]

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