Online #$6$ Begin Date:$(9)/(30)()/(2024)9$:$00$:$00$ AM Due Date:$(10)/(11)()/(2024)9$:$00$:$00$ PM End Date:$(12)/(7)()/(2024)9$:$00$:$00$ PM

Problem $4$: $(10\%$ of Assignment Value$)$

Consider two vectors, vec$($A$)$ and vec$($B$),$ where

vec$($A$)=7\mathrm{.}5$hat$($i$)+3\mathrm{.}6$hat$($j$)$

vec$($B$)=$B$\_($x$)$hat$($i$)+$B$\_($y$)$hat$($j$)$ where $\{($B$=3\mathrm{.}9)$:$\}$

B$\_($x$)>0$

B$\_($y$)>0$

Observe that the components of vec$($A$)$ are known. While the components of vec$($B$)$ are not initially known, the magnitude of vec$($B$)$ is known, and it points into the first quadrant.

Additionally the scalar product between the two vectors is known.

vec$($A$)*$vec$($B$)=16\mathrm{.}05$

Part $($a$)$

What is the x component of the vector vec$($B$)?$ Note: You must find both components before submitting your answer to verify that all conditions are satisfied.

B$\_($x$)=[,]$

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$-$Obtain one equation from the scalar product of vec$($A$)/($b$)$ar $($ and $)/(()/()).$

Obtain a second equation for the magnitude B$.$ Using these two

equations, you can determine two unknowns, B$\_($x$)$ and B$\_($y$).$

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