Question: The points P, Q and R have co-ordinates (2,2,1), (4, 1, 2) and (5,-1,4) respectively. (i) Show that PQ=2i-j+k. (ii) Show that PR =

The points P, Q and R have co-ordinates (2,2,1), (4, 1, 2)

The points P, Q and R have co-ordinates (2,2,1), (4, 1, 2) and (5,-1,4) respectively. (i) Show that PQ=2i-j+k. (ii) Show that PR = 31-3j+3k. (iii) Calculate the vector product PQ x PR. (iv) Calculate the scalar product PQ. PR. (v) Use your answer to (iv) to calculate the angle between the vectors PQ and PR. giving your answer to the nearest degree.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

i To find the vector PQ we subtract the coordinates of point P from point Q Vector PQ Q P 42i 12j 21... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (2 attachments)

663e35f893cf3_959647.pdf

180 KBs PDF File

663e35f893cf3_959647.docx

120 KBs Word File

Students Have Also Explored These Related Mathematics Questions!

Burt's Department Store needs $652,000 to take a cash discount of 2.50/10, net 70. A banker will loan the money for 60 days at an Interest cost of $14,100. a. What is the annual rate on the bank...

Hank's client needs life insurance. He is an aggressive investor, wants to be able to vary his premium payments, is seeking a higher level of interest crediting than ordinarily found in declared -...

CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...

If you dissolve 8.14 grams of calcium chloride, CaCl 2 , in enough water to make 125.0 mL of solution, what is the molarity of the solution?

4. Consider the system of linear equations below. 1 + 212 - 13 = 2 2x1 + 12 - 13 = 2 4x1 + 212 - 213 = 4 Create the augmented matrix [A b]. Row reduce the augmented matrix to row reduced Ech- elon...

1. Find the unit vector along the line joining point (2,4,4) to point (3,2,2). 2. If the position vectors of points T and S are 3ax 2a\" + a, and 4ax + 63. + 221/, respectively, nd a. Coordinates of...

Need help with the documents and excel sheets. I have to follow the instructions but I am stuck on 7-26. Can i get some assistance? Instructions Excel sheet#1 Excel sheet #2 excel sheet#3 File Home...

Find a vector perpendicular to the plane that passes through the points P, Q, and R, and find the area of the triangle PQR. P (-1, 3, 1), Q (0, 5, 2), R(4, 3, -1) A. Vector 1=, AAPQR V165 2 - u2 B....

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 100 N and b = 400 N. Round your answers to one decimal place.) magnitude 360.6 N angle % y Need...

Hello;: help 142. Assuming that, in the multiplication of bacteria, the probability that a bacterium divides into two new bacteria in the interval of time r equals unmatnr) and does not depend on the...

If a = (2, -1, 3) and b = (2, 2, 1), find the following. axb = b x a = Need Help? Read It Watch It Submit Answer 6. [-/2 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHE Find two unit...

Define chase strategy.

Refer to the financial data in Case 105 (on page 611). In analyzing this company, you feel it is important to differentiate between operating success and financing decisions. Required: a. Explain the...

September 2 0 1 7 marked a historic milestone as the US capital account surplus soared to an unprecedented $ 1 8 . 2 billion, signifying that: American companies were exporting a greater volume of...

Modify the HeapIntPriorityQueue class written in this chapter to make it into a three-heap. A three-heap is similar to a binary heap, except that each node is considered to have three children rather...

Modify the HeapIntPriorityQueue class written in this chapter to make it configurable in ways similar to Javas PriorityQueue class. Make it possible for the heap to be a min-heap or max-heap. (If you...

The number of imperfections (scratches, chips, cracks, and blisters) in manufactured custom wood cabinet panels is important both to the customer and to the custom builder. To monitor the...

Calculate the ratio of [Ca 2+ ] to [Fe 2+ ] in a lake in which the water is in equilibrium with deposits of both CaCO 3 and FeCO 3 . Assume that the water is slightly basic and that the hydrolysis of...

Examine the sequences of points in parts af for any trends. a. + + + + + + b. + + + + + + + c. + + + + + d. +++++ ++++++++ e. + + + + + + f. + + + + + + + + +

A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and...

The graph of y = f(x) is shown. It cuts the axes at (0, 4) and (4, 0). a) Sketch y = 3f(x) and give the coordinates where the graph cuts the axes. b) The graph of y = f(x) is transformed to the...

Solve the equation for 0 0 360. cos sin = 0.

Find the sum of the first nine terms of a geometric sequence that has a 3rd term of 45 and a 6th term of 1215.

=+b) Assuming the assumptions for regression inference are met, what do you conclude?

=+R-squared = 59.5% s = 53.79 with 1064 - 2 = 1062 degrees of freedom Variable Coefficient SE(Coeff) t-Ratio P-Value Intercept -3.1169 4.688 -0.665 0.5063 Size 94.4539 2.393 39.465 60.0001...

=+a) Is there an association between the hardness of the water and the mortality rate? Write the appropriate hypothesis.