# 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)

Correct result:

y =  5
z =  0

#### Solution:

$a=(2, y, z) \ \\ b=(-1, 4, 2) \ \\ c=(3, -3, -1) \ \\ \ \\ a.b=0 \ \\ a.c=0 \ \\ \ \\ \ \\ \ \\ 2 \cdot \ (-1)+y \cdot \ 4+z \cdot \ 2=0 \ \\ 2 \cdot \ 3+y \cdot \ (-3)+z \cdot \ (-1)=0 \ \\ \ \\ 4y+2z=2 \ \\ 3y+z=6 \ \\ \ \\ y=5 \ \\ z=-9 \ \\ \ \\ y=5$
$z=0$ We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! 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 linear equation or system of equations and looking for its solution? Or do you have quadratic equation?

## Next similar math problems:

• Linsys2 Solve two equations with two unknowns: 400x+120y=147.2 350x+200y=144
• Null points Calculate the roots of the equation: ?
• Vector Determine coordinates of the vector u=CD if C[19;-7], D[-16,-5].
• Coordinates of vector Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
• Place vector Place the vector AB, if A (3, -1), B (5,3) in the point C (1,3) so that AB = CO
• Warehouses In the three warehouses, a total of 70 tons of grain was stored. In the second warehouse was stored 8.5t less and in the third 3.5t more than in the first. How many tons of grain was stored in each warehouse?
• Geometric sequence 5 About members of geometric sequence we know: ? ? Calculate a1 (first member) and q (common ratio or q-coefficient)
• 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
• Children The group has 42 children. There are 4 more boys than girls. How many boys and girls are in the group?
• 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.
• Men, women and children On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
• Scalar product Calculate the scalar product of two vectors: (2.5) (-1, -4)
• Find d 2 Find d in an A. P. whose 5th term is 18 and 39th term is 120.
• Parabola Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
• 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
• 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
• 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)