Draw the vector C⃗ =0.5A⃗ +2B⃗ . Only the length and orientation of vector C⃗ will be graded. The location of the vector is not important.
The Correct Answer and Explanation is:
To draw the vector 𝐶⃗ = 0.5𝐴⃗ + 2𝐵⃗, it is first necessary to understand vector addition and scalar multiplication.
Step-by-step Explanation:
- Scalar Multiplication:
- The vector 𝐴⃗ is multiplied by 0.5, meaning the resulting vector will have the same direction as 𝐴⃗ but half its magnitude.
- The vector 𝐵⃗ is multiplied by 2, meaning the resulting vector will have the same direction as 𝐵⃗, but its magnitude will be twice as long.
- Vector Addition:
- To add 0.5𝐴⃗ and 2𝐵⃗, place the tail of 2𝐵⃗ at the head of 0.5𝐴⃗. The resultant vector 𝐶⃗ is drawn from the tail of 0.5𝐴⃗ to the head of 2𝐵⃗.
- Geometric Construction:
- Draw vector 0.5𝐴⃗ with correct orientation and half the original length of 𝐴⃗.
- At the tip of 0.5𝐴⃗, draw vector 2𝐵⃗, ensuring it maintains the direction of 𝐵⃗, but has twice the length.
- Connect the start of 0.5𝐴⃗ to the end of 2𝐵⃗. This line represents 𝐶⃗.
- Length and Orientation:
- The length of 𝐶⃗ depends on both the magnitude and direction of 0.5𝐴⃗ and 2𝐵⃗.
- If 𝐴⃗ and 𝐵⃗ point in similar directions, the resulting vector will be longer and close in direction to both.
- If 𝐴⃗ and 𝐵⃗ point in opposite directions, their contributions may partially cancel, shortening the resulting vector and altering its direction.
Now, based on a given diagram or orientation of 𝐴⃗ and 𝐵⃗, the correct drawing of 𝐶⃗ will maintain the direction and scaled length based on the vector sum described above.
Please upload the diagram of 𝐴⃗ and 𝐵⃗, or describe their directions and magnitudes, so the specific drawing of 𝐶⃗ can be generated accurately.
