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

What is the cost per ounce of detergent, A 64-ounce bottle of detergent cos...

A 64-ounce bottle of detergent costs $3.20. What is the cost per ounce of detergent? To ?nd out the cost per ounce, divide the cost through the number of ounces; $3.20 ÷ 64 =

Least common multiple (lcm), Before we look at this, let us learn wha...

Before we look at this, let us learn what a multiple is. Take any number say 3. Multiply this number with natural numbers. We obtain 3, 6, 9, 12, 15, 18,.........

What is the total number of pounds they bought if the total, The student co...

The student council bought two various kinds of candy for the school fair. They purchased 40 pounds of candy at $2.15 per pound and x pounds at $1.90 per pound. What is the total n

How to left shifts and right shifts a graph, Q. How to Left shifts and righ...

Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti

Find the coordinates of c , Plot the points A(2,0) and B (6,0) on a graph p...

Plot the points A(2,0) and B (6,0) on a graph paper. Complete an equilateral triangle ABC such that the ordinate of C be a positive real number .Find the coordinates of C   (Ans: (

Personal assistance needed, I have an original finding on the subject of pr...

I have an original finding on the subject of prime distribution and would like expert help in my endeavors. I have written a paper describing everything in detail and demonstration

Find the generating function, Find the generating function for the number o...

Find the generating function for the number of r-combinations of {3.a, 5.b, 2.c}          Ans:  Terms sequence is given as r-combinations of {3.a, 5.b, 2.c}. This can be writte

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