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

Pair of straight line, The equation ax2 + 2hxy + by2 =0 represents a pair o...

The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+

Tangent, A tangent to a curve at a point is a straight line which tou...

A tangent to a curve at a point is a straight line which touches but does not intersect the curve at that point. A slope of the curve at a point is defined as the

Problem, La proporción de empleados de una empresa que usan su auto para ir...

La proporción de empleados de una empresa que usan su auto para ir al trabajo es 5:16. Si hay un total de 800 empleados, diga la cantidad de autos que se espera que haya estacionad

Basic mathematics, I need help with my homework, I am to the edge right now...

I need help with my homework, I am to the edge right now with this w=5pq/2

Conditional probability - rules of probability, Conditional probability - R...

Conditional probability - Rules of Probability This is the probability associated with combinations of events but given that some prior result has already been achieved with o

Initial conditions to find system of equations, Solve the subsequent IVP. ...

Solve the subsequent IVP. y′′ + 11y′ + 24 y = 0 y (0) =0  y′ (0)=-7  Solution The characteristic equation is as r 2 +11r + 24 = 0 ( r + 8) ( r + 3) = 0

Use mathematical induction and prove equation, 1. Use mathematical inductio...

1. Use mathematical induction to prove whenever n is a positive integer. 2. Use loop invariant to prove that the program for computing the sum of 1,...,n is correct.

Mathematics for finance, 1. XYZ company’s cost function for the next four m...

1. XYZ company’s cost function for the next four months is C = 600,000 + 8Q a) Find the BEP dollar volume of sales if the selling price is br. 10 / unit b) What woul

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