Question

For vector A = 5 i hat + 3 j - 4 k, vector B = - 5 i hat + 5 j + k, and vector C = 2 j - 3 k, find vector C· (vector A - vector B) to three significant figures.

Answer 1

The value of
`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})` in three significant figures is 11.0.

Explanation:

The given vectors are

`\overrightarrow A=5i+3j-4k`

`\overrightarrow B=-5i+5j+k`

`\overrightarrow C=2j-3k`

We need to find the value of
`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})`

Subtraction of two vectors.

`\overrightarrow {A}-\overrightarrow {B}=5i+3j-4k-(-5i+5j+k)`

`\overrightarrow {A}-\overrightarrow {B}=5i+3j-4k+5i-5j-k`

`\overrightarrow {A}-\overrightarrow {B}=(5+5)i+(3-5)j+(-4-1)k`

`\overrightarrow {A}-\overrightarrow {B}=10i-2j-5k`

Dot product of two vectors.

`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=(2j-3k)\cdot (10i-2j-5k)`

`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=(0)(10)+(2)(-2)+(-3)(-5)`

`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=-4+15=11`

Therefore, the value of
`\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})` in three significant figures is 11.0.