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

How many white marbles does the jar contain? , A jar contains 54 marbles e...

A jar contains 54 marbles each of which is blue , green or white. The probability of selecting a blue marble at random from the jar is 1/3  and the probability of selecting a green

Find out solutions to second order differential equations, Find out some so...

Find out some solutions to y′′ - 9 y = 0 Solution  We can find some solutions here simply through inspection. We require functions whose second derivative is 9 times the

Logarithm, I need help with one logarithm problem

I need help with one logarithm problem

Mechanical vibrations, While we first looked at mechanical vibrations we lo...

While we first looked at mechanical vibrations we looked at a particular mass hanging on a spring with the possibility of both a damper or/and external force acting upon the mass.

Two circles touching internally prove that ox:oy=oa:ob, Two circles touchin...

Two circles touching internally at O. OXY, OAB straight lines, the latter passing through the centres. Prove that OX : OY = OA : OB. Given : Two circles touching internally a

Determine series is convergent or divergent by radio test, Determine if the...

Determine if the following series is convergent or divergent by using Radio Test. Solution With this first illustration let's be a little careful and ensure that we h

Definition of natural exponential function, Definition of Natural exponenti...

Definition of Natural exponential function:   The natural exponential function is f( x ) = e x   where, e= 2.71828182845905........ . Hence, since e > 1 we also know that e x

Fraction, Ask question #Minimum 100 words accepted

Ask question #Minimum 100 words accepted

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