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)

Correct 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 wxyz=0 2x+2y=0 w+z=0 x=1  Row3Row1Row3 wxyz=0 2x+2y=0 x+y+2z=0 x=1  Row321 Row2Row3 wxyz=0 2x+2y=0 2z=0 x=1  Row421 Row2Row4 wxyz=0 2x+2y=0 2z=0 y=1  Pivot:Row3Row4 wxyz=0 2x+2y=0 y=1 2z=0  z=20=0 y=11=1 x=202y=202 (1)=1 w=0+x+y+z=0+11=0  w=0 x=1 y=1 z=0  v4=(1,1,0,0)



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Our vector sum calculator can add two vectors given by their magnitudes and by included angle.
Do you have a system of equations and looking for calculator system of linear equations?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions: