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# What is the angle between vectors $2a$ and $4a$? What is the angle between vectors $3a$ and $-5a$?

Last updated date: 21st Jul 2024
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The resultant vector formed when a vector quantity is multiplied by a scalar quantity is the scalar quantity multiplied by the magnitude of the vector. However, the direction is the same. And in the question, the vectors have the magnitude of $2a$ and $4a$ and so the vectors are $2\overrightarrow{a}$ and $4\overrightarrow{a}$. Hence, the direction of both the vectors is $\overrightarrow{a}$ and so they are collinear as they have the same direction and different magnitude. So, the answer to the first part of the question is zero as the vectors are collinear.
When we look at the second part of the question, the magnitude of two vectors are $3a$ and $-5a$ and so using the scalar multiplication of vectors, the two vectors are $3\overrightarrow{a}$ and $-5\overrightarrow{a}$. So, one vector is antiparallel to the other as one of the vectors has a positive direction and the other has a negative direction, so when the vectors are completely opposite in direction, the angle between the vectors is $180{}^\circ$.