Question

If a b c are mutually perpendicular vectors of equal magnitude show that the vector c.D=15

Answer 1

Step-by-step explanation:

hope the attachment helps you to understand the method.....

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Answer 2

Concept:

Vector is a mathematical quantity which can has both direction and magnitude

Unit vector :The vector which has  direction and magnitude equal to 1.

Dot product:

a.b=|a|.|b|.cosα

Cross product:

axb=|a|.|b|.sinα

Given:

a b c are mutually perpendicular vectors of equal magnitude

Find:

Pove that c.D =1

Solution:

|a|=|b|=|c|=k

a.b=b.c=c.a=0

|a+b+c|²=|a|²+|b|²+|c|²+2(ab+bc+ca)

             =3k²

|a+b+c| =√3k

(a+b+c).a=a.a+b.a+c.a

|a+b+c|.|a|.cosα= |a|²

cosα = |a|/|a+b+c|

(a+b+c).a=a.b+b.b+c.

|a+b+c|.|b|.cosβ= |b|²

cosβ = |a|/|a+b+c|

(a+b+c).a=a.c+b.c+c.c

|a+b+c|.|a|.cosγ= |a|²

cosγ = |a|/|a+b+c|

Since a+b+c is equally inclined

∴cosα=cosβ=cosγ

cosα=k/√3k

        =1/√3

c.(a+b+c)=|c|.|a+b+c|.cosα

               =1

Hence, proved

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