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6 Nov 2019
Carry out the following steps to determine the distance between the point P and the line L through the origin with direction v. Find a vector v = 1,b in the direction of line L. Find the position vector u corresponding to point P. Find projvu. Find w = u - projvu and |w|. Explain why |w| is the distance between P and L. P(2,-4); L is y = - x v = 1, u = (Type integers or simplified fractions.) projvu = (Type integers or simplified fractions.) d.w = (Type integers or simplified fractions.) |w| = (Type an exact answer, using radicals as needed.) Why is |w| the distance between the point and the line? The vector w is orthogonal to the line L. When its head is placed at P, its tail is at the origin. Therefore, its length is the same as the distance from the point to the origin, so it is the same as the distance from the point to the line. The vector w is orthogonal to the line L. Since the tail of the vector can be placed at the point P, then its length must be the distance from the point to the line. The vector w is orthogonal to the line L. When its head is placed at P, its tail is on the line. Therefore, its length is the same as that of the perpendicular line segment connecting the point to the line. Show transcribed image text
Carry out the following steps to determine the distance between the point P and the line L through the origin with direction v. Find a vector v = 1,b in the direction of line L. Find the position vector u corresponding to point P. Find projvu. Find w = u - projvu and |w|. Explain why |w| is the distance between P and L. P(2,-4); L is y = - x v = 1, u = (Type integers or simplified fractions.) projvu = (Type integers or simplified fractions.) d.w = (Type integers or simplified fractions.) |w| = (Type an exact answer, using radicals as needed.) Why is |w| the distance between the point and the line? The vector w is orthogonal to the line L. When its head is placed at P, its tail is at the origin. Therefore, its length is the same as the distance from the point to the origin, so it is the same as the distance from the point to the line. The vector w is orthogonal to the line L. Since the tail of the vector can be placed at the point P, then its length must be the distance from the point to the line. The vector w is orthogonal to the line L. When its head is placed at P, its tail is on the line. Therefore, its length is the same as that of the perpendicular line segment connecting the point to the line.
Show transcribed image text Bunny GreenfelderLv2
31 Aug 2019