First bring them to common denominator.
Answer:
Step-by-step explanation:
15 plus 15 plus 15 is 45 - 15 =30
Answer:
50°
Step-by-step explanation:
90°-40°=50°
The square on the angle means 90°.
Hope this helps! :D
Answer:
perpendicular bisector
Step-by-step explanation:
As given by the question
There are given that the vector:

Now,
From the formula to find the unit vector in same direction is:

Then,
![\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7Bv%7D%7D%7B%5Clvert%5Cvec%7Bv%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%5Crvert%7D%20%5Cend%7Bgathered%7D)
Then,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B4%2B9%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5Cend%7Bgathered%7D)
Then,
Rationalize the denominator:
So,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B13%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B%5Csqrt%5B%5D%7B13%7D%282i%7D%2B%5Cvec%7B3j%7D%29%7D%7B13%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B2%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Di%2B%5Cfrac%7B3%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Dj%20%5Cend%7Bgathered%7D)
Hence, the unit vector is shown below: