Physics, asked by kumarisweta482, 1 year ago

Vector A makes equal angle with x,y,z axis .value of its component in form of vector A

Answers

Answered by TheChampion
274
there is a formula for vectors
cos²a+cos²b+cos²c=1
where a,b and c are angles made by the vector with the x,y and z axes respectively.
a=b=c
3cos²a=1
cos²a=1/3
cos a=1/√3
A=1/√3×(i+j+k)
Answered by skyfall63
86

Answer:

\mathrm{A}=\frac{1}{\sqrt{3(\mathrm{i}+\mathrm{j}+\mathrm{k})}}

Solution:

The given system has different sets of axes with which vector A makes equal angle accordingly, so the component will formed in respect to vector A, which can be given by,

Given data suggest that, angle a with x axis = angle b with y axis = angle c with z axis

Thereby, as we know that there is an equation derived for the component for vector which makes angle in 3 dimensions, which is,

\cos ^{2} a+\cos ^{2} b+\cos ^{2} c=1

As, a = b = c

\cos ^{2} a+\cos ^{2} b+\cos ^{2} c=1

\cos ^{2}(3 a)=1

\cos ^{2} a=\frac{1}{3}

\cos a=\frac{1}{\sqrt{3}}

\mathrm{A}=\frac{1}{\sqrt{3(\mathrm{i}+\mathrm{j}+\mathrm{k})}}

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