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franky2727
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how is this done? say angles between 2i -3j -k and 4i+2k-3j got an exam coming up soon and can't find the formula for it anywhere help please?
franky2727 said:not a clue where that determinants coming from, how do you do the determinant of a 3 by 2 matrix
Angles between vectors refer to the measure of the angle formed between two vectors in a multi-dimensional space. They are important in various fields of science, such as physics and engineering, as they help in understanding the relationship between different vectors and their direction.
Angles between vectors can be calculated using the dot product or the cross product of the two vectors. The dot product formula is: θ = cos⁻¹ (a · b / |a||b|), where θ is the angle between the two vectors a and b, and |a| and |b| represent the magnitudes of the two vectors. The cross product formula is: sinθ = |a x b| / |a||b|, where θ is the angle between the two vectors a and b, and |a x b| represents the magnitude of the cross product between the two vectors.
The range of angles between vectors is from 0° to 180°. This range includes acute angles (less than 90°), right angles (exactly 90°), and obtuse angles (greater than 90°). The angle of 0° represents parallel vectors, while the angle of 180° represents antiparallel vectors.
No, angles between vectors cannot be negative. The angle between two vectors is always considered positive, and it represents the smallest angle between the two vectors. However, if the two vectors are pointing in opposite directions, the angle can be considered as either 180° or -180°, depending on the convention used.
Angles between vectors have numerous applications in real-life scenarios. They are used in navigation systems to determine the direction and orientation of objects, in computer graphics to create visual effects and animations, in physics to calculate forces and velocities, and in engineering to design structures and machines. They are also used in mathematics to solve problems related to geometry and trigonometry.