Question

1) Which of the following is not true about vectors.a) Must have magnitude and direction.b) When doing math with vectors, we can usually treat the x and y components independently.c) If several vectors are added together, their order does not matter.d) The magnitude of a vector is the sum of the magnitude of its x and y components.2) Explain briefly your argument or reasoning.

Answer 1

a) A vector must have a magnitude and direction. A physical quantity with only the magnitude is called a scalar.

b) When doing the math we can treat the x and y components independently. We can use only x-component or only y-component for the necessary calculations. For example, the projectile motion. In projectile motion, we use the components of velocities independently.

c) We can add or subtract more than two vectors in any order. For example, If there are 3 vectors, A, B, and C then, from the associative law of vector addition,

`\vec{A}+(\vec{B}+\vec{C})=(\vec{A}+\vec{B})+\vec{C}`

d) The magnitude of the vectors is not the sum of their x and y components. Let vector A be represented as

`\vec{A}=x\hat{i}+y\hat{j}`

Where x and y are the x and y components of vector A respectively. And î and j cap are the unit vectors along the x and y direction respectively.

Then, the magnitude of vector A is given by,

`A=\sqrt[]{x^2+y^2}`

Thus the correct answer is option d. That is the statement in option d is not true.