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yanyin
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find two perpendicular vectors u and v such that each is perpendicular to w = <-4, 2, 5>
Gramm-Schmidt procedure:Originally posted by yanyin
find two perpendicular vectors u and v such that each is perpendicular to w = <-4, 2, 5>
himanshu121 said:No of Unknows a,b,c,d,e,f and no of eq 3.
?U can't find it unless some additional conditions are given
Choose any vector, other than a multiple of w, for u and let v be the cross product of u and w.yanyin said:find two perpendicular vectors u and v such that each is perpendicular to w = <-4, 2, 5>
yanyin said:find two perpendicular vectors u and v such that each is perpendicular to w = <-4, 2, 5>
A vector is a mathematical object that has both magnitude (size) and direction. It is often represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.
To find two perpendicular vectors, you can use the cross product or dot product of two given vectors. If the dot product is equal to zero, then the two vectors are perpendicular. Another method is to use the properties of perpendicular lines, where the dot product of two lines that are perpendicular is always zero.
Yes, there can be multiple pairs of perpendicular vectors. As long as one vector is not a scalar multiple of the other, there will be other vectors that are perpendicular to it.
Two perpendicular vectors can be visually represented on a coordinate plane as two lines that intersect at a 90-degree angle. Alternatively, they can also be represented as two arrows pointing in different directions, with one rotated 90 degrees from the other.
Perpendicular vectors have many applications in mathematics and science. They are used in geometry, physics, and engineering to describe and analyze various systems and phenomena. For example, in physics, the force exerted on an object can be represented as a vector, and if the object is moving in a circular path, the force and velocity vectors would be perpendicular to each other.