Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $-2u ⃗+3v ⃗$.

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Identify the given vectors u⃗ and v⃗ from the first image. Vector u⃗ is pointing upwards, and vector v⃗ is pointing downwards to the right.
2. To find the resultant vector -2u⃗ + 3v⃗, first scale vector u⃗ by -2. This means reversing the direction of u⃗ and doubling its length.
3. Next, scale vector v⃗ by 3. This involves tripling the length of v⃗ while maintaining its direction.
4. Place the scaled vector -2u⃗ on the grid. Then, from the tip of -2u⃗, place the scaled vector 3v⃗.
5. The resultant vector -2u⃗ + 3v⃗ is the vector that starts at the tail of -2u⃗ and ends at the tip of 3v⃗. Draw this vector to complete the sketch.