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Example text
How can one obtain this geometrically? Consider the directed − → line segment, 0u and then, starting at the end of this directed line segment, follow the directed line −−−−−−→ segment u (u + v) to its end, u + v. In other words, place the vector u in standard position with its base at the origin and then slide the vector v till its base coincides with the point of u. The point of this slid vector determines u + v. To illustrate, see the following picture ✶ ✒ ✍ u u+v ✶ v Note the vector u + v is the diagonal of a parallelogram determined from the two vectors u and v and that identifying u + v with the directed diagonal of the parallelogram determined by the vectors u and v amounts to the same thing as the above procedure.
If x = (x1 , · · · , xn ) is called a vector, the vector which is meant is this position vector just described. Another term associated with this is standard position. A vector is in standard position if the tail is placed at the origin. It is customary to identify the point in Rn with its position vector. com 40 Click on the ad to read more Elementary Linear Algebra Fn → is just the distance between The magnitude of a vector determined by a directed line segment − pq the point p and the point q.
Com 31 Click on the ad to read more Elementary Linear Algebra Fn in the picture by the vectors u and v. ✕ u✒ ✗ x3 ■ v u+v ✒ u x2 x1 Thus the geometric significance of (d, e, f ) + (a, b, c) = (d + a, e + b, f + c) is this. com 32 Elementary Linear Algebra Fn with the position vector of the point (d, e, f ) and at its point, you place the vector determined by (a, b, c) with its tail at (d, e, f ) . Then the point of this last vector will be (d + a, e + b, f + c) . This is the geometric significance of vector addition.