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

Answer:

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

Step-by-step 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.