Question

Is this correct? i need to know ASAP

Answer 1

sadly the question is poorly worded, so let's assume "resultant" in this case means addition.

So, from the picture above, we can see the vectors are in component form or namely standard form, so we can say the blue is <3 , 10> and the red one is <6 , 4>.

Well, their addition is just < 3+6 , 10 + 4> or namely the vector <9 , 14>

Now, from that vector where x = 9 and y = 14, its magnitude is just the hypotenuse or radius length, or

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{9}\\ o=\stackrel{opposite}{14} \end{cases} \\\\\\ c=√( 9^2 + 14^2)\implies c=√( 81 + 196 ) \implies c=√( 277 ) \impliedby magnitude`

what's the angle?

`\begin{cases} x=9\\ y=14 \end{cases}\hspace{5em} \tan(\theta )=\cfrac{\stackrel{opposite}{14}}{\underset{adjacent}{9}} \implies \tan^(-1)(~~\tan( \theta )~~) =\tan^(-1)\left( \cfrac{14}{9} \right) \\\\\\ \theta =\tan^(-1)\left( \cfrac{14}{9} \right)\implies \theta \approx 57.3^o\impliedby \textit{direction angle}`

Make sure your calculator is in Degree mode.

Answer 2

Explanation:

See image