Question

Given v=(2,0,-6), w=(3,-2,-4). Find 2(v-3w)

Answer 1

To find 2(v - 3w), subtract 3w from v and multiply the result by 2: (-2, 4, -4)

Step-by-step explanation:

To find 2(v - 3w), we need to first find the values of v - 3w and then multiply it by 2.

To find v - 3w, subtract 3w from v: v - 3w = (2, 0, -6) - (3, -2, -4).

Calculating the subtraction gives us v - 3w = (2 - 3, 0 - (-2), -6 - (-4)) = (-1, 2, -2).

Multiplying this result by 2, we get 2(v - 3w) = 2(-1, 2, -2) = (-2, 4, -4).

Answer 2

The result of 2(v-3w) is the vector (-14, 12, 12). This is obtained by distributing the scalar 2 to both vectors v and -3w and subtracting.

To find 2(v-3w), you distribute the scalar (2) to both vectors v and -3w, and then subtract:

2(v-3w) = 2v - 6w

Now, multiply the scalar 2 by each component of vector \(v\):

`2v = 2 \cdot (2, 0, -6) = (4, 0, -12)`

Similarly, multiply the scalar 6 by each component of vector \(w\):

`\[6w = 6 \cdot (3, -2, -4) = (18, -12, -24)\]`

Now, subtract 6w from 2v:

2v - 6w = (4, 0, -12) - (18, -12, -24)
2v - 6w = (-14, 12, 12)

So, 2(v-3w) = (-14, 12, 12).