# Vector v4

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

Result

v4 = (Correct answer is: (1,-1,0,0))

#### Solution:

$v_{4} \cdot \ v_{1}=0 \ \\ v_{4} \cdot \ v_{2}=0 \ \\ v_{4} \cdot \ v_{3}=0 \ \\ \ \\ \ \\ 1x+1y+1z-1w=0 \ \\ 1x+1y-1z+1w=0 \ \\ 0x+0y+1z+1w=0 \ \\ x=1 \ \\ \ \\ 1 \cdot \ x+1 \cdot \ y+1 \cdot \ z-1 \cdot \ w=0 \ \\ 1 \cdot \ x+1 \cdot \ y-1 \cdot \ z+1 \cdot \ w=0 \ \\ 0 \cdot \ x+0 \cdot \ y+1 \cdot \ z+1 \cdot \ w=0 \ \\ x=1 \ \\ \ \\ w-x-y-z=0 \ \\ w+x+y-z=0 \ \\ w+z=0 \ \\ x=1 \ \\ \ \\ w=0 \ \\ x=1 \ \\ y=-1 \ \\ z=0 \ \\ \ \\ v_{4}=(1,-1,0,0)$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Do you have a system of equations and looking for calculator system of linear equations?

## Next similar math problems:

• Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
• Parallel and orthogonal
I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
• Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
• Vector equation
Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
• Vector
Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
• Vector - basic operations
There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
• Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
• Scalar product
Calculate the scalar product of two vectors: (2.5) (-1, -4)
• Inverse matrix
Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]
• Reference angle
Find the reference angle of each angle:
• Linsys2
Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
• Ball game
Richard, Denis and Denise together scored 932 goals. Denis scored 4 goals over Denise but Denis scored 24 goals less than Richard. Determine the number of goals for each player.
• Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
• Legs
Cancer has 5 pairs of legs. The insect has 6 legs. 60 animals have a total of 500 legs. How much more are cancers than insects?
• Guppies for sale
Paul had a bowl of guppies for sale. Four customers were milling around the store. 1. Rod told paul - I'll take half the guppies in the bowl, plus had a guppy. 2. Heather said - I'll take half of what you have, plus half a guppy. The third customer, Na
• Three unknowns
Solve the system of linear equations with three unknowns: A + B + C = 14 B - A - C = 4 2A - B + C = 0