hence is perpendie 3. From vector N, form a unit vector n in the same direction. 4. Use symmetric equations to find a convenient vector v12 that lies between any two points, one on each line. Again, this can be done directly from the symmetric equations. 5. The dot product of two vectors is the magnitude of the projection of one vector onto the other-that is, A B = || A || B || cos 6, where 6 is the angle between the vectors. Using the dot product, find the %3D projection of vector v12 found in step 4 onto unit vector n found in step 3. This projection is perpendicular to both lines, and hence its length must be the perpendicular distance d between them. Note that the value of d may be negative, depending on your choice of vector v12 or the order of the cross product, so use absolute value signs around the numerator. 6. Check that your formula gives the correct distance of |-25VV198 1.78 between the following two lines:
hence is perpendie 3. From vector N, form a unit vector n in the same direction. 4. Use symmetric equations to find a convenient vector v12 that lies between any two points, one on each line. Again, this can be done directly from the symmetric equations. 5. The dot product of two vectors is the magnitude of the projection of one vector onto the other-that is, A B = || A || B || cos 6, where 6 is the angle between the vectors. Using the dot product, find the %3D projection of vector v12 found in step 4 onto unit vector n found in step 3. This projection is perpendicular to both lines, and hence its length must be the perpendicular distance d between them. Note that the value of d may be negative, depending on your choice of vector v12 or the order of the cross product, so use absolute value signs around the numerator. 6. Check that your formula gives the correct distance of |-25VV198 1.78 between the following two lines:
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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