An insect is crawling along the line

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:1.) Two insects are crawling along different lines in R3. At time t (in minutes) the first insect is at the point (x, y, z) on the line x = 6+t, y = 8 – t, z = 3 +t. Also at time t the second insect is at the point (x, y, z) on the line x = 1+t, y = 2+t, z = 2t. Assume that distances are given in inches. a) How far apart are the insects at t = 0? b) How far 1.) Two insects are crawling along different lines in R3. At time t (in minutes) the first insect is at the point (x, y, z) on the line x = 6+t, y = 8 – t, z = 3 +t. Also at time t the second insect is at the point (x, y, z) on the line x = 1+t, y = 2+t, z = 2t. Assume that distances are given in inches. a) How far apart are the insects at t = 0? b) How far apart are the insects at t = 6? c) What is the closest the two insects will ever get to each other? Previous question Next question

An insect is crawling along the line \(\vec r = 6\hat i + 2\hat j + 2\hat k+\lambda(\hat i - 2\hat j + 2\hat k)\)and anotherinsect is crawling along the line \(\vec r = - 4\hat i - \hat k + \mu (3\hat i - 2\hat j-2\hat k).\)At what points on the lines should they reach so that the distance between them is the shortest? Find the shortest possible distance between them. The given lines are non-parallel lines. There is a unique line segment PQ (P lying on one and Q on the other) at right angles to both lines. PQ is the shortest distance between the lines. Hence, the shortest possible distance between the insects = PQ The position vector of P lying on the line \(\vec r = 6 \hat i + 2\hat j + 2\hat k + \lambda (\hat i - 2\hat j + 2\hat k)\)is \((6 + \lambda )\hat i + (2 - 2\lambda)\hat j + (2 + 2\lambda)\hat k\)for some λ The position vector of Q lying on the line \(\vec r= -4\hat i - \hat k + \mu (3\hat i - 2\hat j - 2\hat k)\)is \((-4 + 3\mu )\hat i + (-2\mu )\hat j + (-1 - 2\mu )\hat k\)for some μ \(\vec \) \(= \sqrt 9\) The given lines are non-parallel lines. There is a unique linesegment PQ (P lying on one and Q on the other, which is at right angles to both the lines. PQ is the shortest distance between the lines. Hence, the shortest possible distance between the insects = PQ The position vector of P lying on the line The position vector of the points, at which they should be so that the distance between them is the shortest, are Categories • • (31.9k) • (8.8k) • (764k) •...

134. An insect is crawling along the line r = 6 i ^ + 2 j ^ ​ + 2 k ^ + λ ( i ^ − 2 j ^ ​ + 2 k ^ ) and another insect is crawling along the line r = − 4 i ^ − k ^ + μ ( 3 i ^ − 2 j ^ ​ − 2 k ^ ). At what points on the lines should they reach so that the distance between them is the shortest? Find the shortest possible distance between them. 134. An insect is crawling along the line r = 6 i ^ + 2 j ^ ​ + 2 k ^ + λ ( i ^ − 2 j ^ ​ + 2 k ^ ) and another insect is crawling along the line r = − 4 i ^ − k ^ + μ ( 3 i ^ − 2 j ^ ​ − 2 k ^ ). At what points on the lines should they reach so that the distance between them is the shortest? Find the shortest possible distance between them. Updated On Mar 10, 2023 Topic Vector and 3D Subject Mathematics Class Class 12 Answer Type Video solution: 16 Upvotes 1633 Avg. Video Duration 7 min

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:15.) Two insects are crawling along different lines in R. At time t (in minutes) the first insect is at the point (x, y, z) on the line x 6+ t, y 8-t, z 3 + t. Also at timet the second insect is at the point (x, y,z) on the line x 1+t, y=2+ t, z= 2t. Assume that distances are given in inches. How far apart are the insects at t 0? a) How far apart are the 15.) Two insects are crawling along different lines in R. At time t (in minutes) the first insect is at the point (x, y, z) on the line x 6+ t, y 8-t, z 3 + t. Also at timet the second insect is at the point (x, y,z) on the line x 1+t, y=2+ t, z= 2t. Assume that distances are given in inches. How far apart are the insects at t 0? a) How far apart are the insects at t 6? b) how atyek deayane What is the closest the two insects will ever get to each other? c) Previous question Next question

This problem has been solved: Solutions for Chapter 11.5 Problem 111E: Distance Two insects are crawling along different lines in three-space. At time t (in minutes), the first insect is at the point (x, y, z) on the linex = 6 + t, y = 8 − t, z = 3 + t.Also, at time t, the second insect is at the point (x, y, z) on the linex = 1 + t, y = 2 + t, z = 2t.Assume distances are given in inches.(a) Find the distance between the two insects at time t = 0.(b) Use a graphing utility to graph the distance between the insects from t = 0 to t = 10.(c) Using the graph from part (b), what can you conclude about the distance between the insects?(d) How close do the insects get? … Get solutions Get solutions Get solutions done loading • CHP • CH1.P.S • CHP.1 • CH1.1 • CH1.2 • CH1.3 • CH1.4 • CH1.5 • CH1.R • CH2.P.S • CHP.2 • CH2.1 • CH2.2 • CH2.3 • CH2.4 • CH2.5 • CH2.6 • CH2.R • CH3.P.S • CHP.3 • CH3.1 • CH3.2 • CH3.3 • CH3.4 • CH3.5 • CH3.6 • CH3.7 • CH3.8 • CH3.9 • CH3.R • CH4.P.S • CHP.4 • CH4.1 • CH4.2 • CH4.3 • CH4.4 • CH4.5 • CH4.6 • CH4.R • CH5.P.S • CH5.1 • CH5.2 • CH5.3 • CH5.4 • CH5.5 • CH5.6 • CH5.7 • CH5.8 • CH5.R • CH6.P.S • CH6.1 • CH6.2 • CH6.3 • CH6.4 • CH6.R • CH7.P.S • CH7.1 • CH7.2 • CH7.3 • CH7.4 • CH7.5 • CH7.6 • CH7.7 • CH7.R • CH8.P.S • CH8.1 • CH8.2 • CH8.3 • CH8.4 • CH8.5 • CH8.6 • CH8.7 • CH8.8 • CH8.R • CH9.P.S • CH9.1 • CH9.2 • CH9.3 • CH9.4 • CH9.5 • CH9.6 • CH9.7 • CH9.8 • CH9.9 • CH9.10 • CH9.R • CH10.P.S • CH10.1 • CH10.2 • CH10.3 • CH10.4 • CH10.5 • CH10.6...

An insect is crawling along the line r ˉ = 6 i ^ + 2  ^ ​ + 2 k ^ + λ (  ^ − 2 j ^ ​ + 2 k ^ ) and another insect is crawling along the line r ˉ = − 4 i ^ − k ^ + μ ( 3 i ^ − 2 j ^ ​ − 2 k ^ ). At what points on the lines should they reach so that the distance between them is the shortest? Find the shortest possible distance between them. Q35. Find the product ⎣ ⎡ ​ 1 0 3 ​ − 1 2 − 2 ​ 2 − 3 4 ​ ⎦ ⎤ ​ ⎣ ⎡ ​ − 2 9 6 ​ 0 2 1 ​ 1 − 3 − 2 ​ ⎦ ⎤ ​ x + 3 z = 9 , − x + 2 y − 2 z = 4 and 2 x − 3 y + 4 z = − 3 SECTION E (This section comprises of 3 case-study/passage-based questions of 4 marks each with two sub-parts. First two case study questions have three sub-parts (i), (ii), (iii) of marks 1 , 1 , 2 respectively. The third case study question has two sub-parts of 2 mark each.) * 12 Views: 5,429 A ( 2 i ^ − j ^ ​ + k ^ ) , B ( i ^ − 3 j ^ ​ − 5 k ^ ) , C ( 3 i ^ − 4 j − 4 k ^ ) are the vertices of a right angled triangle. Solation We have A B = ( 1 − 2 ) i ^ + ( − 3 + 1 ) j ^ ​ + ( − 5 − 1 ) k ^ = − i ^ − 2 j ^ ​ − 6 k ^ BC = ( 3 − 1 ) i ^ + ( − 4 + 3 ) j ^ ​ + ( − 4 + 5 ) k ^ = 2 i ^ − j ^ ​ + k ^ CA = ( 2 − 3 ) i ^ + ( − 1 + 4 ) j ^ ​ + ( 1 + 4 ) k ^ = − i ^ + 3 j ^ ​ + 5 k ^ ​ Views: 5,170 P and Q be 3 i ^ − j ^ ​ + 2 k ^ and i ^ + 2 j ^ ​ − 4 k ^, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are ( 4 , − 1, 2 ) and ( − 2 , 1 , − 2 ), respectively. Let lines PR and QS intersect at T. If the vector TA is perpendicular to both PR a...