Find a point Q such that (i) P Q has the same direction as v. (ii) P Q has the opposite direction as v. Here:

Q: Show that one of the lines givenby 6x² - xy - 12y² = 0 coincides with one of %3D the lines givenby…

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Q: For what values of z and y is orthogonal to both (-1 and

A: Remark: We know that two vectors are orthogonal if they are perpendicular to each other. i.e., the…

Q: A straight river flows east at a speed of 10 mi/h. A boater starts at the south shore of the river…

A: Let u be the relative speed of the motorboat, with respect to  the water. If v be the speed of the…

Q: In the accompanying diagram, trans- versal RS intersects parallel lines +> XY and WZ at E and H,…

A: Given: RS is transversal line that means it intersects two parallel lines (XY and WZ). Therefore…

Q: Plot the points A = ( - 1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment…

A: We have the following information    We have to plot the points A = ( - 1, 8) and M = (2, 3) in…

Q: Tom, Andrew, and Tobey are in a standoff. Tom aims his webslinger at Andrew N70°E 14 meters away,…

A: This can be solved using cardinal directions and law of cosines and also using the concept of…

Q: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

Q: Q2: -A meter stick in the x'y' plane makes angles of 45° with the x' and y' axes. O' and the meter…

A: The angle that the metre stick make with x axis is

Q: = 1, where, 0 <c < r. r?-q?

A:

Q: Consider the two following lines in R. (;)-) 1 + y = 2x – 5 and y 2 - t (a) Find the point where…

A: The standard form of a linear equation is ax+by+c=0. For two intersecting lines: a1x+b1y+c1=0 and…

Q: The tangent of the acute angle between the lines y = 4x – 3 and y =x-5 is 4. IA 2 D

A: Two lines are given as : y = 4x - 3 and y = x - 5

Q: The TOUR de France is happening on the 26th June 2021 from BREST to MÜR DE BRETAGNE. Mark cycles…

A: The relationship between the distance, speed, and time is defined using the formula:…

Q: Use the side-splitter theorem to solve for x in the triangle below.

A: Given,

Q: Find the acute angles between the lines y = √3x - 1, y = -√3x + 2 Find the length and direction…

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Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 4 feet per second,…

A: The rate of flying is 4 ft/sec. The toal time is 1.5 minutes, i.e. 90 second. The distance covered…

Q: Line QS bisects ∠PQT, and line QP  and line QR are opposite rays. If m∠PQT = 60  and m∠PQS = 4x +…

A: ∠PQT=60° ; ∠PQS=4x+14And ∠PQS=12 ∠PQT                      Because QS…

Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the slope of the…

A: Here ABCD is a trapezoid and AB parallel BC which also parallel to the X axis

Q: Find the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.

A: Two vectors are parallel if the angle between them is 0 or π. That is, the vectors are pointing in…

Q: Sketch parallelogram-INDY with diagonals intersecting at point P in the box below on the left. If IP…

A: Given,           A parallelogram INDY with diagonals intersevting at point P.           IP=3x,…

Q: In the figure, the straight lines L:ax+ by = 1 and L,:y = x+c intersect at the point A on the…

A: The line are intersecting at x-axis co-ordinates of point A is m,0Now we find intersecting point if…

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given 7, -2

Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: Given that the point (5, 0) a) symmetric with respect to the x axis Substitute the coordinate -y for…

Q: A man on an island k km south of a straight shoreline wants to reach a point on the shore c km west…

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Q: Find the Cartesian equation of the locus of points satisfying PA + PB = 12, where A is the point…

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Q: determine the points that are symmetric with respect to (a) the x axis, (b) the y axis, and (c) the…

A: (a) Consider the point (-3, 1). Recall that to find the point that is symmetric about the x-axis, we…

Q: A straight river flows east at a speed of 8 mi/h. A boater starts at the south shore of the river…

A: Let the boater starts from A. And he wants to go to B. It has to go in direction of AC to reach to…

Q: If VW is not parallel to UX, what is VW?

A: Clearly from the figure we can see that the base angles are same. So this figure is an isoceles…

Q: A man is flying in a hot-air balloon in a straight line at a constant rate of 7 feet per second,…

A:

Q: An airplane is flying at an airspeed of 600 km/hr in a cross-wind at 50 km/hr that is blowing from…

A: Given: A  = The Airspeed     = the speed of airplane in wind. = 600 km/h  (Black vector) w = The…

Q: 4- Find the direction and direction from the point (1, 3) for which the values off do not change,…

A: 4)Given isfx,y=e2y arc tan3y3x at point 1,3A function  fx,y has no change in any direction that is…

Q: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

Q: A parallelegram PRQS has P(-1,3), S(4,2), Q(5,-1). Find R

A:

Q: Suppose ABC is reflected across the line x = -1. What are the coordinates for the image of A?

A: There is no change in y coordinates while taking mirror image across x = k.

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: If the direction vector of a line is 3i + 2j and the gradient of another line is s 5/2, find the…

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Q: Combined equation of OA,OB is ax² +2hxy + by² + 2(x² + y²) = 0

A:

Q: 8. A plane must begin its descent when it is 80 feet above the ground and 250 feet from the airport.…

A: Given:- A plane must begin its descent when it is 80 feet above the ground and 250 feet from the…

Q: Show that the two lines X= 1+4t X = 2 + St and y= 5-4t J= 4 - 36 Z: -1+ SE 2: 5+t Rind the distance…

A: There are two equations of line:

Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the equation of the bisectiors of the obtuse angle between the lines x + y – 5 = 0 and x – 7y…

A: x+y-5=0  .................(1)rewrite the given equation as:-x-y+5=0 x-7y+7=0   ............(2)

Q: x+2y=12 x-4y=4 what is the angle that lies between two lines and is closest to the y-axis?

A: Tantheta = |(a1b2- b1a2)/(a1a2+b1b2)|

Q: find the angle between the planes Sメ4y-21。メーマy ト

A: Given the equation of two planes 5x+y−z=10x−2y+3z=−1

Q: Prove that the equation ax² + 2hxy+by² + 2gx+2 fy+c=0 wi h²2 = ab and bg2 = af?. Also find the…

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Q: (a) Oppositely directed to v = (3, -4) and half the length of v. %3D W3= (?, ?) (b) Length V5 and…

A: To Find : a) A vector which is oppositely directed to v=&lt;3,-4&gt; and half the length of vb) A…

Q: Luna calculates d, and also the distance d, from the point E to the line through D and F and notices…

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Q: (b) Use the cross product to derive the distance formula between the point Q and the line l PQ × PŘ…

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