Question

In: Advanced Math

Find the intersection of the line passing through P=(21,21) and Q(−63,168) and the line passing through...

Find the intersection of the line passing through P=(21,21) and Q(−63,168) and the line passing through points R(21,0) and S(0,21) using vectors.

Solutions

Expert Solution

First, we have written down the equation of lines passing through the given points in vector form. Then, to find the point of intersection of the two lines, we have to equate the x and y components of both the lines, as explained in the solution.


Related Solutions

Find the intersection of the line passing through P=(-10,-6,-6) and Q(50,-18,-18) and the plane passing through...
Find the intersection of the line passing through P=(-10,-6,-6) and Q(50,-18,-18) and the plane passing through points R(-10,0,0), S(0,-6,0) and T(0,0,-6).
Find the symmetric image of P(−28,18,20) about the plane passing through Q(0,0,0) and perpendicular to the...
Find the symmetric image of P(−28,18,20) about the plane passing through Q(0,0,0) and perpendicular to the vector n=[−5,5,2].
Find the line that passes through the point (0, 1) and through the point of intersection...
Find the line that passes through the point (0, 1) and through the point of intersection of the two lines  and
4(a). Find the equation y = ax + b of the line passing through (2,3) and...
4(a). Find the equation y = ax + b of the line passing through (2,3) and (5,8). (Your answer should be an equation of the form y = ax + b, for some constants a and b.) (b) Find the equation y = ax^2 + bx + c of the parabola passing through the points (-2, -6), (1,6), and (3,4). (Your answer should be an equation of the form y = ax^2 + bx + c, for some constants a,...
(a) Find the equation of the plane passing through the point P(0, 0, 5) and the...
(a) Find the equation of the plane passing through the point P(0, 0, 5) and the line x = 1 + t, y = 1 − t, z = 4 − 5t. (b) Find parametric equations for the line passing through point (1, 2, 3) and parallel to the line x = 2 − 3t, y = 4 + t, z = 2t.
The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway...
The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 12 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection. a. Enter an exact number as an integer, fraction, or decimal. μ = b. σ =  (rounded to two decimal places) c. What is the probability that the speed of a car is at most 26 mph? d. What is the probability that the...
A traffic engineer believes that the number of cars passing through a certain intersection between 2...
A traffic engineer believes that the number of cars passing through a certain intersection between 2 and 6 pm on weekdays follows a normal distribution with mean 750 and standard deviation 100. A new highway is opened, and it is hypothesized that the number or cars passing through the intersection should decrease as a result. A sample of 15 weekdays is taken, and the mean number of cars passing through the intersection is 710. Decide whether this reduction in traffic...
Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3,...
Let L be the line passing through the point P=(−3, −4, 2) with direction vector →d=[−3, 3, 0]T. Find the shortest distance d from the point P0=(1, −5, −1) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed to give an exact value for your answer. d = 0 Q = (0, 0, 0)
Find the equation of the line through the point P = (0,2,−1) that is perpendicular to...
Find the equation of the line through the point P = (0,2,−1) that is perpendicular to both ⃗v = 〈3,0,1〉 and ⃗w = 〈1,−1,2〉. v and w are vectors by the way
McMahon and Associates, an engineering firm, counted 300 cars passing through an intersection. The observations showed...
McMahon and Associates, an engineering firm, counted 300 cars passing through an intersection. The observations showed that 175 of the cars were traveling in the northbound/southbound lanes and 55 of those turned left at the intersection. The remaining 125 cars were traveling in the eastbound/westbound lanes and 30 of those turned left at the intersection. Use the count data to estimate the probability that a randomly chosen car arriving at the intersection is traveling in the northbound/southbound lanes or is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT