Question

Perform the indicated operation on the following vectors. a=2j+k b=-3i+5j+4k z=i-3j-k 3a+7b-4z -25i +53j +27k X

Answer 1

Perform vector operations by distributing the scalar to each vector component and adding/subtracting the corresponding components. The resulting vector is -17i + 53j + 27k.

Step-by-step explanation:

To perform the indicated operations on the given vectors, we can use the distributive property of vector addition and scalar multiplication.

1. First, calculate 3a = 3(2j + k) = 6j + 3k.
2. Next, calculate 7b = 7(-3i + 5j + 4k) = -21i + 35j + 28k.
3. Then, calculate 4z = 4(i - 3j - k) = 4i - 12j - 4k.
4. Finally, add the three resulting vectors: 3a + 7b - 4z = (6j + 3k) + (-21i + 35j + 28k) + (4i - 12j - 4k) = -17i + 53j + 27k.

Therefore, the resulting vector is -17i + 53j + 27k.