Answer:
a) The magnitude of the vector is changed my a multiplication factor of 2
b) The direction of the vector is changed by a multiplication factor of 1
Step-by-step explanation:
Let the first component of a vector be x
Let the second component of the vector be y
The vector, A = xi + yj
The magnitude of the vector A will be:
![|A|\text{ = }\sqrt[]{x^2+y^2}](https://img.qammunity.org/2023/formulas/physics/college/rr7ewiyp865bc9qwlyzimws1z2fbc3sj22.png)
The direction of the vector A will be:

If each component of the vector is doubled
Double of the first component = 2x
Double of the second component = 2y
The new vector, B = 2xi + 2yj
The magnitude of the new vector B will be:
![\begin{gathered} |B|\text{ = }\sqrt[]{(2x)^2+(2y)^2} \\ |B|\text{ = }\sqrt[]{4x^2+4y^2} \\ |B|\text{ = }\sqrt[]{4(x^2+y^2)} \\ |B|\text{ = 2}\sqrt[]{x^2+y^2} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/o63ev6nkb31s5p9m7t90bfsembtr25j1u9.png)
The direction of the new vector B will be:

Since:
![|A|\text{ = }\sqrt[]{x^2+y^2}\text{ and }|B|=2\sqrt[]{x^2+y^2}](https://img.qammunity.org/2023/formulas/physics/college/nf7i4ufquh3q2k8u4ohp40lxdq6emhm3oi.png)
then:
|B| = 2|A|
The maginitude of the vector is double. That is, it is changed by a multiplication factor of 2
Since:

then:
The direction of the vector does not change. That is, the multiplicative factor is 1