SpletTaking L to be the x-axis, the line integral between consecutive vertices (x i,y i) and (x i+1,y i+1) is given by the base times the mean height, namely (x i+1 − x i)(y i + y i+1)/2. The sign of the area is an overall indicator of the direction of traversal, with negative area indicating counterclockwise traversal. SpletThe lines 3 x − 1 = 4 y − 3 = 5 z − 4 and 3 x − 1 = 1 y − 3 = − 2 z − 4 are coplanar Reason If two lines are perpendicular to each other, then these are coplanar.
If for some α∈R, the lines L1:x+1/2=y 2/ 1=z 1/1 and L2:x+2
Splet6. Show that the lines L1: x¡4 2 = y +5 4 = z ¡1 ¡3 L2: x¡2 1 = y +1 3 = z 2 are skew. Solution: Write the equation in parametric form. L1 : x = 2t+4; y = 4t¡5; z = ¡3t+1 L2 : x = s+2; y = 3s¡1; z = 2s The lines are not parallel since the vectors ~v1 = h2;4;¡3i and ~v2 = h1;3;2i are not parallel. Next we try to flnd intersection point ... SpletSolution Equation of the line through P (2,1,3) is x−2 a = y−1 b = z−3 c ...(i) As (i) is ⊥ to lines x−1 1 = y−2 2 = z−3 3 and x −3= y 2= z 5 ∴ a+2b+3c =0 and −3a+2b+5c= 0 Solving for a,b,c, we have a 10−6 = b −9−5 = c 2+6 ⇒ a 4= b −14 = c 8 ⇒ a 2= b −7= c 4 ∴ from (i), we get required cartesian form i.e. x−2 2 = y−1 −7 = z−3 4 cosy hub amber flashing cloud light
on which of the following lines does the point (7, 1) lie? a. y - 5x ...
SpletThe equation of the plane containing the two lines x 1/2 = y+1/ 1 = z/3andx/ 1= y 2/3 = z+1/ 1 is Byju's Answer Standard XI Mathematics Equation of a Plane : Normal Form The equation ... Question The equation of the plane containing the two lines ( x - 1) 2 = ( y + 1) - 1 = z 3 and x - 1 = ( y - 2) 3 = ( z + 1) - 1 is A 8 x + y – 5 z – 7 = 0 B Splet10. sep. 2024 · 47) Show that the lines of equations x = t, y = 1 + t, z = 2 + t, t ∈ R, and x 2 = y − 1 3 = z − 3 are skew, and find the distance between them. Answer: 48) Show that the lines of equations x = − 1 + t, y = − 2 + t, z = 3t, t ∈ R, and x = 5 + s, y = − 8 + 2s, z = 7s, s ∈ R are skew, and find the distance between them. SpletIf for some α∈R, the lines L1: x+1 2 = y−2 −1 = z−1 1 and L2: x+2 α = y+1 5−α = z+1 1 coplanar, then the line L2 passes through the point: Q. If lines L1: x 2= y−2 −1 = z−1 1 and L2: x−1 α = y+2 2+α = z −1 are coplanar, then the line L2 passes through point (s) Q. If a line passes through the points (2, 5) and (-1, -1), equation of the line is . Q. cosy house socks for visitors