Final answer:
The statement about using the Pythagorean theorem to calculate the length of a resultant vector from two perpendicular vectors is true. Given vectors of 6 cm and 3 cm, the theorem allows us to determine the resultant vector's length as approximately 6.71 cm. So, the given statement is A. True
Step-by-step explanation:
Understanding the Pythagorean Theorem in Vector Calculation
When dealing with vectors, the Pythagorean theorem can be a powerful tool.
Specifically, it is used to calculate the magnitude (or length) of a resultant vector when the vectors that are being added are perpendicular to each other.
For instance, if we have two orthogonal vectors with lengths of 6 cm and 3 cm, by applying the Pythagorean theorem:
c2 = a2 + b2
We can calculate the length of the resultant vector (c) as follows:
c2 = 62 + 32 => c2 = 36 + 9 => c2 = 45
Thus, c = √45, which is approximately 6.71 cm.
In this context, the statement 'We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other.' is true.
Therefore, the given statement is A. True