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

Accumulated amount , $26,000 is spended for two years. In the first year it...

$26,000 is spended for two years. In the first year it gets interest at 8.3% p.a. compounded semi annually. In the same year the rate of interest changes to 7.5% p.a. compounded da

Example to understanidng of multiplication, 6-year-old Rahul wasn't able to...

6-year-old Rahul wasn't able to understand multiplication when it was thrust upon him in school. His mother discussed this problem with some of us. On the basis of suggestions that

Differentiate hyperbolic functions, Differentiate following functions. (...

Differentiate following functions. (a)  f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t

System of first order equations, Consider the Van der Pol oscillator x′′...

Consider the Van der Pol oscillator x′′- µ(1 - x 2 )x′ + x = 0 (a) Write this equation as a system of first order equations (b) Taking µ = 2, use MatLab's routine ode45 to

Euler equations with an auxiliarty condition - shortest path, 1. Finding th...

1. Finding the shortest path btween any two points on the surface of a sphere but use the method of the euler equations with an auxiliarty condition imposed? Question2:

Find the 14th term in the arithmetic sequence. 60, Find the 14th term in t...

Find the 14th term in the arithmetic sequence. 60, 68, 76, 84, 92

Explain histogramsin details, Explain Histogramsin details? Another way...

Explain Histogramsin details? Another way to display frequencies is by using a histogram. The following is an example of a histogram using the data from the previous example:

Hours, jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how l...

jeff left hartford at 2:15 pm and arrived in boston at 4:45 pm how long did the drive take him?

Vectors, Find the magnitude of the following vectors: 5i+7j

Find the magnitude of the following vectors: 5i+7j

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