If the position vectors of the points A, B, C, D are a = i+j+k, b=...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
If the position vectors of the points A, B, C, D are a = i+j+k, b= 2i + 3j, c = 3i + 5j – 2k, d = k -j, show the line segments AB and CD are parallel and find the ratio of their lengths. Given the two vector combinations a+ 4b = 4i + 4j + 6k, a- 2b = i+7j + 3k, find a and b. The position vectors of the points A. B and C are a = 3i -j-k, b= 2i + 2j +7k and c = 5i + 2j- 3k. Find (i) the position vector of the centroid of A, B and C. (ii) the position vectors of the points P and Q which divide AB internally and externally in the ratios AP: PB = 1 : 2 and AQ : QB = -2:1. Determine whet her the vectors a = 2i – 3j + 5k, b = 31+j- 2k and c = i- 7j + 12k are linearly dependent or linearly independent. Show that the vectors a = 3i-j+4k, b = i- 3j– 2k and e = 4i – 3j+2k are linearly independent. Find mumbers a, 3 and 7 such that d 2i + 3j - k can be expressed in the form d= aa +3b+ye. Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5,0,6) are collinear, (ii) the four points P(2,-1, 1), Q(1,3.-2), R(-2, 1,-3) and S(3,2,0) are coplanar. If a = i+ 3j - k, b 2i + 4j- 2k and c = -i+ 2j + 4k, find a number A such that d = a +b + Ac is parallel to the yz-plane. If the position vectors of the points A, B, C, D are a = i+j+k, b= 2i + 3j, c = 3i + 5j – 2k, d = k -j, show the line segments AB and CD are parallel and find the ratio of their lengths. Given the two vector combinations a+ 4b = 4i + 4j + 6k, a- 2b = i+7j + 3k, find a and b. The position vectors of the points A. B and C are a = 3i -j-k, b= 2i + 2j +7k and c = 5i + 2j- 3k. Find (i) the position vector of the centroid of A, B and C. (ii) the position vectors of the points P and Q which divide AB internally and externally in the ratios AP: PB = 1 : 2 and AQ : QB = -2:1. Determine whet her the vectors a = 2i – 3j + 5k, b = 31+j- 2k and c = i- 7j + 12k are linearly dependent or linearly independent. Show that the vectors a = 3i-j+4k, b = i- 3j– 2k and e = 4i – 3j+2k are linearly independent. Find mumbers a, 3 and 7 such that d 2i + 3j - k can be expressed in the form d= aa +3b+ye. Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5,0,6) are collinear, (ii) the four points P(2,-1, 1), Q(1,3.-2), R(-2, 1,-3) and S(3,2,0) are coplanar. If a = i+ 3j - k, b 2i + 4j- 2k and c = -i+ 2j + 4k, find a number A such that d = a +b + Ac is parallel to the yz-plane.
Expert Answer:
Related Book For
College Physics Reasoning and Relationships
ISBN: 978-0840058195
2nd edition
Authors: Nicholas Giordano
Posted Date:
Students also viewed these mathematics questions
-
If you know the position vectors of a particle at two points along its path and also know the time it took to move from one point to the other, can you determine the particles instantaneous velocity?...
-
Businesses A, B. C. and D are plotted on a Strategic Group Map with geographic scope (national, regional, local) on the vortical asis and dutribufion level (internive. selective, exclusive) on the...
-
Find the best alternative using incremental IRR analysis. A B D Initial cost $2000 4000 5000 3000 Annual benefit 800 1300 500 400 Salvage value 1400 2000 1500 3000 Life, in years 6 4 MARR required 6%...
-
Class Median Midpoint, x Income, I 19.5 $12,965 An individual's income varies with age. The table shows the median income I of individuals of different age groups within the United States for a...
-
What is meant by commercialization of schools? What are the various areas in which commercialization can occur and what are the major concerns?
-
Consider a coal-fired steam power plant that produces 300 MW of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of 5 MPa and 450C and a...
-
On March 13, 2009, Juan Mendez Sr. was admitted to a nursing facility. On that day, a doctor employed by the facility determined the father lacked the capacity to give informed consent or make...
-
Manilow Corporation operates in an industry that has a high rate of bad debts. Before any year-end adjustments, the balance in Manilow's Accounts Receivable account was $555,000 and the Allowance for...
-
An owner arrives to collect her dog's prescription for ampicillin tablets. The dog weighs 23 kg and the dose of ampicillin suggested by the vet is 15 mg/kg/t.i.d. You have the tablets available in...
-
Prepare the retained earnings statement by dragging and dropping the appropriate accounts into their correct sections. Revenue Service Revenue Expenses Kleene Window Washing Inc. Income Statement For...
-
TMH Ltd. is a manufacturing company engaged in the manufacturing of valves. They have been in the business for last 5 years and have been manufacturing only one type of valves. They started their...
-
A close family friend will sell you his coffee shop for $250,000, with "seller financing," at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month...
-
We sold 10 call option contracts (recalling that one contract represents 100 shares of stock). As of today the delta is 0.6. How many shares of stock should we hold to be delta neutral? The delta for...
-
How do changing family structures, including the rise of single-parent households, cohabitation, and delayed marriage, influence social cohesion, intergenerational relationships, and caregiving...
-
How can a single-parent home be impacted due to the family system laws, regulations, policies, and education?
-
1. Assume that you invest $3,249.66 and your investment grows at 9% for each of the first 2 years. At that point, you learn that the investment is likely to only earn 6% for the remaining 3 years....
-
______________ between mentors and trainees is crucial for honesty and understanding. Group of answer choices Gossiping History Background checks Dialogue
-
Experiment: Tossing four coins Event: Getting three heads Identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when...
-
A squirrel is resting in a tall tree when it slips from a branch that is 50 m above the ground. It is a very agile squirrel and manages to land safely on another branch after only 0.50 s. What is the...
-
The charge per unit length on a glass rod is = -7.5 C/m. If the rod is 2.5 m long, how many excess electrons are on the rod?
-
Two blocks with the same volume but different densities are in a lake as shown in Figure Q10.14. Block m 1 floats at the surface with a portion above the water level, and block m 2 floats underwater....
-
Assuming = 5, compute (a) P(5) (b) P(X < 5) (c) P(X 5) (d) P(5 X 7) The random variable X follows a Poisson process with the given mean.
-
(a) Graph the binomial probability distribution with n = 10 and p = 0.2. Comment on the shape of the distribution. (b) Graph the binomial probability distribution with n = 10 and p = 0.5. Comment on...
-
According to CTIA, 41% of all U.S. households are wireless-only households. In a simple random sample of 300 households, determine the mean and standard deviation number of wireless-only households....
Study smarter with the SolutionInn App