inha said:The cross product is zero for perpendicular vectors so the cartesian unit vectors would satisfy that as i x j = i x k =0.
Yeah, the cross product is zero for parallel vectors. So (1,1,1) x (2,2,2)= (1,1,1) x (3,3,3) = (0,0,0) is a solution.Antiphon said:That's all wrong. The dot product is zero for perpendicular vectors.
The cross product is i x j = k.
Vectors a, b, and c are mathematical quantities that have both magnitude and direction. They are represented by arrows, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction.
To solve for vectors a, b, and c, you will need to use vector algebra and trigonometry. This involves finding the components of the vectors, using the Pythagorean theorem to find the magnitude, and using trigonometric functions to find the direction.
Solving for vectors a, b, and c is important in many fields of science and engineering, such as physics, mechanics, and navigation. Vectors are used to represent physical quantities and their direction, making them essential for solving many problems in these fields.
Sure! Let's say we have a vector a with a magnitude of 5 and a direction of 30 degrees from the horizontal. We can use trigonometry to find its x and y components, which would be ax = 5cos30° = 4.33 and ay = 5sin30° = 2.5. Then, we can use the Pythagorean theorem to find the magnitude of the vector, which would be sqrt(4.33^2 + 2.5^2) = 5.
Solving for vectors a, b, and c is commonly used in real-world applications such as navigation, engineering, and physics. For example, calculating the forces acting on an object or finding the direction and speed of a moving object would require solving for vectors a, b, and c.