![\textbf{A}×\textbf{B}= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%C3%97%5Ctextbf%7BB%7D%3D%2068%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%2052%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
Explanation:
Given:
![\textbf{A} = 5\hat{\textbf{i}} - 7\hat{\textbf{j}} - 3\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%20%3D%205%5Chat%7B%5Ctextbf%7Bi%7D%7D%20-%207%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%203%5Chat%7B%5Ctextbf%7Bk%7D%7D)
![\textbf{B} = -4\hat{\textbf{i}} + 4\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%5Ctextbf%7BB%7D%20%3D%20-4%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%204%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
The cross product
is given by
![\textbf{A}×\textbf{B} = \left|\begin{array}{ccc}\hat{\textbf{i}} & \hat{\textbf{j}} & \hat{\textbf{k}} \\\:\:5 & -7 & -3 \\ -4 & \:\:4 & -8 \\ \end{array}\right|](https://tex.z-dn.net/?f=%5Ctextbf%7BA%7D%C3%97%5Ctextbf%7BB%7D%20%3D%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%26%20%5Chat%7B%5Ctextbf%7Bj%7D%7D%20%26%20%5Chat%7B%5Ctextbf%7Bk%7D%7D%20%5C%5C%5C%3A%5C%3A5%20%26%20-7%20%26%20-3%20%5C%5C%20-4%20%26%20%5C%3A%5C%3A4%20%26%20-8%20%5C%5C%20%5Cend%7Barray%7D%5Cright%7C)
![= \left|\begin{array}{cc}-7 & -3\\\:4 & -8\\ \end{array}\right|\:\hat{\textbf{i}}\:+\:\left|\begin{array}{cc}-3 & \:\:5\\-8 & -4\\ \end{array}\right|\:\hat{\textbf{j}}\:+\: \left|\begin{array}{cc}\:\:5 & -7\\-4 & \:\:4\\ \end{array}\right|\:\hat{\textbf{k}}](https://tex.z-dn.net/?f=%3D%20%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D-7%20%26%20-3%5C%5C%5C%3A4%20%26%20-8%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bi%7D%7D%5C%3A%2B%5C%3A%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D-3%20%26%20%5C%3A%5C%3A5%5C%5C-8%20%26%20-4%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bj%7D%7D%5C%3A%2B%5C%3A%20%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D%5C%3A%5C%3A5%20%26%20-7%5C%5C-4%20%26%20%5C%3A%5C%3A4%5C%5C%20%5Cend%7Barray%7D%5Cright%7C%5C%3A%5Chat%7B%5Ctextbf%7Bk%7D%7D)
![= 68\hat{\textbf{i}} + 52\hat{\textbf{j}} - 8\hat{\textbf{k}}](https://tex.z-dn.net/?f=%3D%2068%5Chat%7B%5Ctextbf%7Bi%7D%7D%20%2B%2052%5Chat%7B%5Ctextbf%7Bj%7D%7D%20-%208%5Chat%7B%5Ctextbf%7Bk%7D%7D)
<span>reflection, rotation, translation</span>
Answer:
Approximate height of the building is 23213 meters.
Explanation:
Let the height of the building be represented by h.
0.02 radians = 0.02 × ![\frac{180^{o} }{\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B180%5E%7Bo%7D%20%7D%7B%5Cpi%20%7D)
= 0.02 x (180/
)
0.02 radians = 1.146°
10.5 km = 10500 m
Applying the trigonometric function, we have;
Tan θ = ![\frac{opposite}{adjacent}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Badjacent%7D)
So that,
Tan 1.146° = ![\frac{h}{10500}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%7D%7B10500%7D)
⇒ h = Tan 1.146° x 10500
= 2.21074 x 10500
= 23212.77
h = 23213 m
The approximate height of the building is 23213 m.
Negative charge (it has more protons than electrons)
B. Gamma rays
Gamma rays have highest energy