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

Simultaneous equations by substitution, Simultaneous equations by substitut...

Simultaneous equations by substitution: Solve the subsequent simultaneous equations by substitution. 3x + 4y = 6      5x + 3y = -1 Solution: Solve for x: 3x = 6

Equivalent or equal sets, Equivalent or Equal sets Two sets C and D are ...

Equivalent or Equal sets Two sets C and D are said to be equal whether every member of set C belongs to D and every member of set D belongs also to C.

how large a sample is necessary to have a standard error, If the populatio...

If the population standard deviation is o=8, how large a sample is necessary to have a standard error that is: a.  less than 4 points? b.  less than 2 points? c.  less than 1 poin

Interval of validity, The interval of validity for an IVP along with initia...

The interval of validity for an IVP along with initial conditions: y(t 0 ) = y 0 or/and y (k) (t 0 ) = y k There is the largest possible interval on that the solution is va

How to converting decimals to percents, How to Converting Decimals to Perce...

How to Converting Decimals to Percents ? To convert a decimal to a percent: Move the decimal point two decimal places to the right. Place a percent sign after the resulting

Circles, assignment on theorems on circle for class 9

assignment on theorems on circle for class 9

Word or term for, An irregular perimeter to the circumference of a circle s...

An irregular perimeter to the circumference of a circle such as a protrusion

Transportation and assignment problem, what is transportation and assignmen...

what is transportation and assignment problem. give the computer application of transportation and assignment problem

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