Final answer:
The length of the resultant vector from the addition of two perpendicular vectors can indeed be found using the Pythagorean theorem. A vector can form a right-angled triangle with its components.
correct option is b) False
Step-by-step explanation:
The question being asked can be understood as pertaining to the properties of vectors and their application in geometry, specifically in relation to the Pythagorean theorem and vector addition. When we deal with vectors, several properties and theorems are commonly used to solve for unknown quantities such as lengths and angles.
Pythagorean Theorem in Vector Addition
For the question, 'True or False - 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,', the answer is true. When two vectors are at right angles to each other, they form a right-angled triangle. The Pythagorean theorem can then be used to calculate the magnitude of the resultant, which would be the hypotenuse of the triangle.
Vector Components and Right-Angled Triangles
The statement, 'A vector can form the shape of a right angle triangle with its x and y components,' is also true. Any vector in a two-dimensional space can be broken down into x and y components, which will essentially form the legs of a right-angled triangle, with the vector itself being the hypotenuse.
Angles of Resultant Vectors
In response to the statement, 'If only the angles of two vectors are known, we can find the angle of their resultant addition vector,' it is typically false without additional information such as the magnitudes of the vectors, because just knowing the angles isn't sufficient to determine the resultant vector's direction or magnitude.