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[" Inustration 1.28The axes of coordinat...

[" Inustration 1.28The axes of coordinates are rotated about the "z" -ajis through an angle of "pi4" in the "],[" anticotockwise direction and the compoonents of a vector asqrt(2) ",3sqrt(2),4" .Prove that the components of "],[" the same vector in the original system are- "-1,5,4" ."],[" Sol.If "hat i,hat j,hat k" are the new unit vectors along the coordinate axes,then "]

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The axes of coordinates are rotated about the z-axis though an angle of pi//4 in the anticlockwise direction and the components of a vector are 2 sqrt(2), 3 sqrt(2), 4. Prove that the components of the same vector in the original system are -1,5,4.

The axes of coordinates are rotated about the z-axis through an angle of pi//4 in the anticlockwise direction and the components of a vector are 2sqrt2, 3sqrt2, 4 . Prove that the components of the same vector in the original system are -1, 5, 4 .

The axes of coordinates are rotated about the z-axis though an angle of pi//4 in the anticlockwise direction and the components of a vector are 2sqrt(2), 3sqrt(2), 4. Prove that the components of the same vector in the original system are -1,5,4.

A vector 4hat i+3hat j rotates about its tail through an angle 53^(@) in anticlockwise direction then the new vector is