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

the bug should start to move in order to increase, The temperature at the ...

The temperature at the point (x, y) on a metal plate is given by the function f(x, y) = x 3 + 4xy + y 2 where f is in degrees Fahrenheit and x and y are in inches, with the origin

Fractions, how do i multiply and divide fractions?

how do i multiply and divide fractions?

Math, there is 22 owls . my mom gave me 6 more . how many owls do they have...

there is 22 owls . my mom gave me 6 more . how many owls do they have

Simple equations, three times the first of the three consecutive odd intege...

three times the first of the three consecutive odd integers is 3 more than twice the third integer. find the third integer.

Describe differance between mean vs. mode, Describe differance between Mean...

Describe differance between Mean vs. Mode ? Every set of numbers or data has a mean and a mode value. The mean is the average value of all the numbers in the set. The mode is t

Generic rectangles and greatest common factors, miaty and yesenia have a gr...

miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.

What is the probability a 3 will be rolled and a tail tossed, A die is roll...

A die is rolled and a coin is tossed. What is the probability that a 3 will be rolled and a tail tossed? Find the probability of each event separately, and then multiply the an

Demerits and merit-the median, The median Merits i.  This shows t...

The median Merits i.  This shows the centre of a described set of data ii.  Knowledge of the determination of the median may be extended to find out the quartiles i

digraph of r, Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb...

Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere

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