Let v1= [ 0.5 ] 0.5 0.5 0.5 , v2= [ -0.5 ] 0.5 0.5 -0.5 , and v3= [ 0.5 ] 0.5 -0

ID: 3211289 • Letter: L

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Let v1= [ 0.5 ] 0.5 0.5 0.5 , v2= [ -0.5 ] 0.5 0.5 -0.5 , and v3= [ 0.5 ] 0.5 -0.5 -0.5 . Find a vector v4 in R4 such that the vectors v1, v2, v3, and v4 are orthonormal

Explanation / Answer

Conditions for orthonormality of a set of vectors: -> Vectors are unit vectors -> Vectors are mutually perpendicular let V4 = x i + y j + z k for mutually perpendicular vector dot product =0 take dot product of V4 with V1,V2,V3 and also |V4| =1 apply these conditions to get the values of x,y,z this will give you the required vector. ...feel free to ask any query regarding this question.

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Let v1= [ 0.5 ] 0.5 0.5 0.5 , v2= [ -0.5 ] 0.5 0.5 -0.5 , and v3= [ 0.5 ] 0.5 -0

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