I think nowhere. So the book answer must be a mistake.Crystal037 said:
Your relevant equation is wrong, unless by ab, you mean the scalar product of vector a and vector b .Crystal037 said:
If two vectors ##\vec a## and ##\vec b## are orthogonal, then ##\vec a\cdot\vec b=0 \Rightarrow |\vec a + \vec b | = |\vec a - \vec b | ##SammyS said:
Try this instead.Crystal037 said:
Yes then the answer comes as 3.SammyS said:
The resultant of two orthogonal vectors is a vector that represents the combined effect of the two original vectors. It is found by using the Pythagorean theorem to calculate the magnitude and trigonometric functions to determine the direction.
The components of the resultant are calculated by using the dot product and cross product of the two original vectors. The dot product gives the magnitude of the resultant in the direction of one of the vectors, while the cross product gives the magnitude in the direction perpendicular to both vectors.
Yes, the resultant of two orthogonal vectors can be zero if the two vectors are equal in magnitude but opposite in direction. This is known as a zero vector or a null vector.
The angle between two orthogonal vectors can be found by using the inverse trigonometric functions of the dot product and cross product. The dot product gives the cosine of the angle, while the cross product gives the sine of the angle.
The resultant of two orthogonal vectors is commonly used in physics and engineering, such as calculating the force of two perpendicular forces acting on an object. It is also used in navigation and mapping, as well as in computer graphics for creating 3D images and animations.