Which one of the following points lies on the line x = -(t + 6), y = (- (6 t)) – 4, z = 2 t – 4? о (-7, —10, —2) O (-7,2, –2) о (-5, —10, —6) о (-5, —8, —2) |

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

A:

Q: Which of the following equation of the line is perpendicular to 10x + 6y = O 3x + 5y + 7 = 0 O 5x -…

A:

Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find a function r(t) that describes the line segment from P(8,7,8) to Q(0,7,5) (inclusively). r(t) =…

A: See the details solution below

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

A:

Q: For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3y = 1?

A:

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x = 2s + 2, y = s + 3,…

A: Answer

Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Find the point (xo, yo) on the line 4x + 9y = 12 that is closest to theong1n.

A: Given: 4x+9y=12 Let the distance between the point (x0, y0) and origin be D As it is given that the…

Q: Consider the relation between r and y defined by the equation r4/3+y4/3 = 10. Find the r-intercept…

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: find value(s) of k so that the lines described by 3x = 2y+11 and kx = 40 - 6y are perpendicular

A:

Q: T Find the tangeut line to the curve 1 2rg+ 12 at the point (2. 1).

A:

Q: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: I Fnd the polnt of intersection of the following lines and graph them 2r+3y=6 and x-y-3

A: Let us find the point of intersection of the given lines in the next steps.

Q: An object moves along a horizontal line according to s (t) = 5t° – 2t², when is V increasing and…

A: In the given question, concept of derivative is applied. Derivative The derivative expresses the…

Q: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

A:

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find the distance from the point S= (1, 2, 1) to the line x = 2-t, y=-1+2t, and z=2+ 2t.

A:

Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

A:

Q: Q6) Find the distance from the point S= (1, 2, 1) to the line x = 2 -t, y=-1 + 2t, and z= 2 + 2t.

A:

Q: A molecule is moving along the x-axis such that at any time t 2 0 (in seconds), its position from…

A:

Q: Find the distance from the point P(-1,2,4) to the line given by x=2t y=1+t z=3t

A: Given query is to find the the distance between point and the line

Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

A:

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: find equation for the line threugh (el) and farullel to z-axis. Q3 :

A: To determine: The equation of the line passing through the point (1,1,1) and parallel to the z-axis.…

Q: Find an equation for the linear function g(z) which is perpendicular to the line 7z – 6y = 12 and…

A: Given the equation of a line 7x−6y=12

Q: [a] Find the shortest distance from the point (2, -1, 4) to the straight line x = 2, y = 3+tand z =…

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: Find the per pendicualar olistace from the P (5,6) to the line -2xr+3Y+4=0.

A: Formula for perpendicular distance is as below : Given :-2x+3y+4=0Ax+By+C=0A=-2B=3C=4 Point  (m , n…

Q: Q2) find the distance between two lines L1: x= 1 +4t, y=5 - 4t, z=-1+5t L2: x=2 + 8t, y=4 - 3t, z-5…

A: Method 1:

Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

A:

Q: Q3: Let L: x-2+3t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

A: given line is                                                         L1: x=2+3t, y=2t-1, z=4tM:…

Q: And the sope and y-ntercept (r possble) of the Ine. Lir- 14y - 2 Arst, we must rewrite the equation…

A: Given  13x-14y = 28 equation of a line in slope intercept form is given by  y = mx+c         where m…

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: show.. that. the line in.which. and. .5Xm2y.Z==.0. jntersect..is

A: Equation of the plane: - In three-dimensional space, a plane surface is represented by an equation…

Q: f(x) =Tx-L, C17,4) find an eguation e tancend line to the arraph Given point of the off at the

A:

Q: If xy + 6ey = 6e, find the value of y'' at the point where x = 0.

A: Ans.        xy+6ey =6e          xdydx+y+6eydydx=0       xd2ydx2+dydx1+dydx+6ey d2ydx2+6eydydx2=0at…

Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

A:

Q: Q3: Let L;: x-2+33t, y 2t-1, z-4t and M: x+2y+z-11, and let (p) be thus point of intersection. Find…

A:

Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

A:

Q: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

A:

Q: Find the point (Xo, Yo) on the line 4x + 6y = 12 that is closest to the origin. (Xo, Yo) =

A:

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

A:

Q: X. xy ds where C is the straight line from (2,3) to (4,0).

A: Given: The curve C is the straight line from 2,3 to 4,0, To find: The value of ∫Cxy2ds.

Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7-2t y=t z = 9+t

A:

Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…