Vector v4

Find the vector v4 perpendicular to the vectors
v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1)

Final Answer:

v4 = (1,-1,0,0)

Step-by-step explanation:

v4   v1 = 0 v4   v2 = 0 v4   v3 = 0  1x+1y+1z1w=0 1x+1y1z+1w=0 0x+0y+1z+1w=0 x=1  1 x+1 y+1 z1 w=0 1 x+1 y1 z+1 w=0 0 x+0 y+1 z+1 w=0 x=1  wxyz=0 w+x+yz=0 w+z=0 x=1  Row2Row1Row2 2x+2y=0  Row3Row1Row3 x+y+2z=0  Row321 Row2Row3 2z=0  Row421 Row2Row4 y=1  Pivot:Row3Row4  z=20=0 y=11=1 x=202y=202 (1)=1 w=0+x+y+z=0+11=0  w=0 y=1 z=0  v4=(1,1,0,0)



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