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.

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erinna erinna · Answer 1 · 2020-01-16T06:15:30+01:00

Answer:

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

Step-by-step explanation:

The given vectors are

[tex]\overrightarrow A=5i+3j-4k[/tex]

[tex]\overrightarrow B=-5i+5j+k[/tex]

[tex]\overrightarrow C=2j-3k[/tex]

We need to find the value of [tex]\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})[/tex]

Subtraction of two vectors.

[tex]\overrightarrow {A}-\overrightarrow {B}=5i+3j-4k-(-5i+5j+k)[/tex]

[tex]\overrightarrow {A}-\overrightarrow {B}=5i+3j-4k+5i-5j-k[/tex]

[tex]\overrightarrow {A}-\overrightarrow {B}=(5+5)i+(3-5)j+(-4-1)k[/tex]

[tex]\overrightarrow {A}-\overrightarrow {B}=10i-2j-5k[/tex]

Dot product of two vectors.

[tex]\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=(2j-3k)\cdot (10i-2j-5k)[/tex]

[tex]\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=(0)(10)+(2)(-2)+(-3)(-5)[/tex]

[tex]\overrightarrow {C}\cdot (\overrightarrow {A}-\overrightarrow {B})=-4+15=11[/tex]

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