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

Real numbers on every line, Make a file called "testtan.dat" which has 2 li...

Make a file called "testtan.dat" which has 2 lines, with 3 real numbers on every line (some negative, some positive, in the range from-1 to 3).  The file can be formed from the edi

#algebra, what is the answer of 6_5x9_4x3(1_2)

what is the answer of 6_5x9_4x3(1_2)

What is factorial, Q. What is Factorial? A factorial is a number with a...

Q. What is Factorial? A factorial is a number with a factorial sign, !, after it. 5! is read "five factorial." 3! is read "three factorial." The factorial of a natural

Calculate the volume of rectangular piece of cardboard, 1. A rectangular pi...

1. A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Quan. literacyprofiency, 3.20 euros per kilogram, 1 kilogram =2.2 pounds an...

3.20 euros per kilogram, 1 kilogram =2.2 pounds and current exchange rate is $1=0.9 euros. what is the price per pound?

Outer automorphism, (a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is ca...

(a) An unordered pair fm; ng with 1 ≤ m ≠ n ≤ 6 is called a duad. List the 15 duads. (b) There are 15 ways to partition {1, ......, 6 } into 3 duads, such as { {1; 2}, {3, 4},

How to find the range of a function, How to Find the range of a function ? ...

How to Find the range of a function ? Sigh. Students ask me this all the time. They don't want an explanation, they want a procedure. "Tell me the steps!" Unfortunately, th

Types of sets, NULL/ VOID/ EMPTY SET A set which has no element is know...

NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and

Definition of the definite integral , Using the definition of the definite ...

Using the definition of the definite integral calculate the following.                                                             ∫ 0 2  x 2   + 1dx Solution Firstly,

Show that 8 - 10 + 21= 0, If A, B and P are the points (-4, 3), (0, -2) and...

If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans :   AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2

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