Vectors, Mathematics

Assignment Help:

The angles between three non-zero and non coplanar vectors a,b and c are

α between b and c

and β between c and a

and γ between a and b.

The vector u and v are defined by u=(aXb)Xc;

v=aX(bXc).

If u is perpendicular to v, then show that either

a is perpendicular to c

or cosβ=cosα.cosγ .
 
solution) Given that u=(axb)xc, v=ax(bxc), both the vectors are equal in magnitude because of the associated law, and u.v=0, therefore it must be true that a.c=0, because excluding a and c , b is not situated at right angles so angle between a and c is 90.


Related Discussions:- Vectors

Evaluate the length of the diagonal of the print, A framed print measures 3...

A framed print measures 36 by 22 in. If the print is enclosed by a 2-inch matting, Evaluate the length of the diagonal of the print? Round to the nearest tenth. See Example.

Adding fractions, please give the answer 1/9+1/3 with working out

please give the answer 1/9+1/3 with working out

Definition of vertical asymptote, Vertical asymptote Definition : The funct...

Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a .   x→a- Note as well that it

What is the larger dimension in inches of the frame, Jessica has a picture ...

Jessica has a picture in a frame with a total area of 288 in2. The dimension of the picture without the frame is 12 in through 14 in. What is the larger dimension, in inches, of th

Steps for alternating series test, Steps for Alternating Series Test Su...

Steps for Alternating Series Test Suppose that we have a series ∑a n and either a n = (-1) n b n or a n = (-1) n+1 b n where b n > 0 for all n.  Then if,   1.

Determine the probability, Determine the Probability From a pack of pl...

Determine the Probability From a pack of playing cards what is the probability of; (i)  Picking either a 'Diamond' or a 'Heart' → mutually exclusive (ii) Picking either

What is the average temperature on the celsius scale, Peggy's town has an a...

Peggy's town has an average temperature of 23° Fahrenheit in the winter. What is the average temperature on the Celsius scale? If the total amount for both is 80, after that th

Collecting and interpreting data, Q. How to Collecting and interpreting dat...

Q. How to Collecting and interpreting data? Ans. Collecting and interpreting data is the most important job of a statistician. There are many types of studies and differe

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd