Answer :

(i)

Let, r⃗ = î - j + k̂

The direction ratios of the vector r⃗ = 1, - 1, 1

And, |r⃗ | = √ ((1)^{2} + ( - 1)^{2} + (1)^{2})

= √3

The direction cosines of the vector r⃗

So,

Thus, angles made by with the coordinate axes are given by

(ii)

Let, r⃗ = 0 î + j - k̂

The direction ratios of the vector r⃗ = 0, 1, - 1

And, |r⃗ | = √ ((0)^{2} + (1)^{2} + ( - 1)^{2})

= √2

The direction cosines of the vector r⃗

So,

Thus, angles made by with the coordinate axes are given by

(iii)

Let, r⃗ = 4î + 8 j + k̂

The direction ratios of the vector r⃗ = 4, 8, 1

And, |r⃗ | = √ ((4)^{2} + (8)^{2} + (1)^{2})

= √81

= 9

The direction cosines of the vector r⃗

So,

Thus, angles made by with the coordinate axes are given by

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