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

Differntial equation, Verify Liouville''''s formula for y "-y" - y'''' + y ...

Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?

Decimals, what is 0.875 of 2282?

what is 0.875 of 2282?

Modeling with first order differential equations, We here move to one of th...

We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a

Find the ways to choose a president and a secretary, Q. There are 10 studen...

Q. There are 10 students on the school debating team. How many different ways can the team choose a president and a secretary? Ans. There are 10 choices for the president

Proper fractions, find all the kinds of fraction and give an 10 examples.

find all the kinds of fraction and give an 10 examples.

The ratio of boys to girls at the dance was 3:4, The ratio of boys to girls...

The ratio of boys to girls at the dance was 3:4. There were 60 girls at the dance. How many boys were at the dance? Use a proportion comparing boys to girls at the dance. Boys/

Indices, advantages and disadvantages of paasche and laspeyres indices

advantages and disadvantages of paasche and laspeyres indices

Class 10, chapter permutation & combination ex :4.6

chapter permutation & combination ex :4.6

Math reasoning, The probability that a certain region in mexico will be hit...

The probability that a certain region in mexico will be hit by a hurricane in any given year is .06. What is the probability that the region will be hit by at least one hurricane i

How to solve lim 1-cos(x)/1-cos(4x) as x tends to zero, Use L''hopital''s r...

Use L''hopital''s rule  since lim X-->0  1-cos(x)/1-cos(4x)  is in the indeterminate form 0/0 when we apply the limt so by l''hoptital''s rule differentiate the numerator and den

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