Question

Could a set of three vectors in ℝ⁴?

a) Vector Space Analysis
b) ℝ⁴ Vector Set
c) Three Vector Existence
d) Vectors in ℝ⁴

Answer 1

The magnitude of a vector sum is not necessarily greater than that of its components due to directional properties of vectors. The magnitude of a vector with x and y components can be found using the Pythagorean theorem, leading to a magnitude of 5 cm for the given components.

Step-by-step explanation:

When dealing with vectors, it's important to understand that the magnitude of the sum of the vectors does not necessarily have to be greater than the magnitudes of the individual vectors added together. This is because vectors have both magnitude and direction. Adding more vectors to the equation does not always result in a vector with greater magnitude.

For practice problem 5, to find the magnitude of a vector with given x and y components, you use the Pythagorean theorem:

• The vector's x-component is 4 cm.
• The vector's y-component is 3 cm.

The magnitude (M) is then calculated as: M = √(4^2 + 3^2) = √(16 + 9) = √25 = 5 cm.

The correct answer is b. 5 cm.