Question

What is a 3d angle ?

Answer 1

Hint:Here in this question we have defined a 3d angle. So, firstly we know the definition of angle and 3d. Then we know the definition of 3d angle. We can measure the angle, for that we have a formula. Hence this will be the required solution for the given question.

Complete answer:
In geometry, an angle can be defined as the figure formed by two rays meeting at a common endpoint. An angle is represented by the symbol $$\mathrm{\angle }$$. The 3d means three dimensional. In a three dimensional axis there are three lines which are perpendicular to each other. These lines will meet at one common point. The three coordinates are x- coordinate, y - coordinate and z - coordinate. The all three coordinates have both positive and negative values. The three dimensional axis is represented as

Now consider the question, we have to define a 3d angle. 3d angle means the angle formed by the lines in three dimensional space. We can use vectors to measure angle in 3d space.Since we have a formula and it is given by
$$\Rightarrow A.B=|A||B|\cos x$$
Rewriting the above formula, we have
$$\Rightarrow \cos x={\displaystyle \frac{A.B}{|A||B|}}$$
The x represents the angle so we have
$$\therefore x={\cos }^{-1}\left({\displaystyle \frac{A.B}{|A||B|}}\right)$$
Here $A$ and $B$ are vectors, the angle can be calculated by using the above formula.

Note:While solving the problems related to this topic, the student must know the tables of the trigonometric ratios. The angles have a SI unit and they are degree and radian. Suppose we term which is not present in the table of trigonometric ratio we can write the term as it is.