Question

Help me guys please with this question

Answer 1

`\mid \vec C\mid=31.9`

Step-by-step explanation:

Consider the vectors:

`\vec A=9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}}`

`\vec B=-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}}`

Calculate the magnitude of

`\vec C=-2\vec B-\vec A`

Substitute the values of the vectors:

`\vec C=-2(-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}})-(9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}})`

Operate and remove parentheses:

`\vec C=19\mathbf{\hat{i}}+26.8\mathbf{\hat{j}}-9.4\mathbf{\hat{i}}+3.6\mathbf {\hat{j}}`

Operating both components separately:

`\vec C=9.6\mathbf{\hat{i}}+30.4\mathbf{\hat{j}}`

Now find the magnitude of C:

`\mid \vec C\mid=√(9.6^2+30.4^2)`

`\mid \vec C\mid=√(1016.32)`

`\mathbf{\mid \vec C\mid=31.9}`