Show that the sum of the squares of the direction cosines of a line through the origin is equal to 1 Hint: Let (a, b, c) be a point on the line at distance 1 from the origin. Write the direction cosines in terms of (a, b, c).

Q: Find the distance between the points P = (1, 3) and Q = ( - 4, 2).

A: We have to find the distance between point P(1,3) and Q(-4,2)

Q: -) that passes through (-1,3) that is parallel to 2x – 5y = 1

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Q: Calculate the distance from the point P(9,4,3) to the line which contains points A(1,0,1) and…

A: we use  product rule to find distance between line and point

Q: 11a) Are the two lines parallel? Show work 4 (3, 2) -30] 2. (5,-1) 【け1.-B12 2

A: Given: Co-ordinates of line l1=(-3,0) and (3,2) Co-ordinates of line l2=(-1,-3) and (5,-1)

Q: find the nature of triangle formed by the lines x2- 3y2 =0 and X=2

A: Nature of triangle is isoscelene

Q: Determine the symmetric equations of line that passes through the points B and С.

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Q: Show that the lines whose direction cosines are given by l+m+n=0,2mn+3nl-5lm=0 are perpendicular to…

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Q: Plot each pair of points and compute the distance between them: (1, 4) and (3, 2)

A: Here given points  x1, y1=1, 4, x2, y2=3, 2 Use the distance formula between two points…

Q: Find the value of a that makes lines u and v parallel. 70° 14+12x v 10

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Q: Find nature of the triangle formed by the lines x2-3y2=0 and x=2

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Q: What value of x would prove that lines /and m are parallel?

A: Given that lines m and l are parallel.

Q: A ladder leans against wall so that its slope is 1.80. The top of the ladder is 9 vertical feet…

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Q: Prove that the point (1,11),(2,15), and (-3,-5) are collinear and find the equation of the straight…

A: Let the given points be A (1,11), B (2,15), and C (-3,-5). Evaluate the slope of the line AB as…

Q: Show that the perpendicular let fall from any points on the straight line 7x - 9y + 10 = 0 upon the…

A: See the details solution in below

Q: The distanced of a point P to the line through points A and B is the length of the component of AP…

A: Answer

Q: Find the distance between the points P(, 6,7) and Q(, 1,, 5)

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Q: Sketch the second order spline that fits the end points PO (0,0), P2(9,4) and tangents intersection…

A: Here we need to sketch the second order spline that fits the end points P0 0,0, P2 9,4 and tangents…

Q: plot the ordered pairs(2,-3) and (3,5) on the Cartesian Plane. draw a line that passes through these…

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Q: Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0).…

A: To find the distance from point D to line l.

Q: Find the distance from the point A to the line through the points B and C where A, B, d C have the…

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Q: if (u, v) and (s, t) are two distinct points in the plane, what is the distance between them?…

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Q: The distanced of a point P to the line through points A and B is the length of the component of AP…

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Q: Find the distance between the points (1, −7) and (4, 2).

A: To find the distance between the given points

Q: Show that the line containing the points(a,b) and (b,a) , a ≠b is perpendicular to the line…

A: The objective is to show that the line containing the points a,b and b,a , a≠b is perpendicular to…

Q: At what point on the line y = -b does the line segment from (0, 0) to (a,0) subtend the greatest…

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Q: Find the value of a that makes lines u and v parallel. 130° x+ 135 y O 5

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Q: Assume that all lines that appear tar 1. Find AB

A: We can find the length of AB in the following step

Q: Find the angle between the straight-lines 3x – 2y + 9 = 0 and 2x + y – 9 = 0 ?

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Q: find the equation of  the perpendicular biceptor of the segment joining (4,2) and (-2, 6).

A: Let ( x1,y1) and ( x2,y2) be (4,2) and (-2,6) respectively

Q: Line l is an auxiliary line parallel to m

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Q: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: The distance from (6,-7, 10) to yZ-plane is

A: Concepts let (x, y, z) be a point then  1) distance of the point from XY plane is…

Q: Consider the points P(-4, 1, 0, 3), Q(0, 3, 1, -4), R(-2, 1, 5, 0). RS PQ is parallel to Find the…

A: Given:- P=(-4,1,0,3) ,Q=(0,3,1,-4) and R=(-2,1,5,0) To find the point S in R4 whose third component…

Q: Two lines that cross at a point are called v lines.

A: Two lines can either cross or run parallel to each other.

Q: Find the length of the transverse axis if the length of the semi-transverse axis is 55.

A: This question can be solved if we know the relation between transverse axis and semi transverse…

Q: Write down equation of the line in space passing through the points Po(1,0,0) and P (0, 1, 1).

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Q: Explain why the lines below are parallel. li: (х, у, г) %3D e2: (х, у, г) %3D(3, 7, — 2) + (-1, - 2,…

A: Given: l1:(x,y,z)=(2,3,4)+n(1,2,−3)l2:(x,y,z)=(3,7,−2)+r(−1,−2,3)

Q: Find the distance from the Point A (,2,1) to the line joining the too Points BB (o,5,2), C( 3,2,7).

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Q: determine the acute angle (in degrees) between the lines 4x + 7y +9 = 0 and 2x + 5y - 1 = 0

A: Solve by slope method

Q: Which are parallel.

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Q: Plot each pair of points and compute the distance between them:(a) (1, 4) and (3, 2) (b) (2, 1) and…

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Q: what is the geometric plàce of points multiplication two given whose of their distance to the lines…

A: Let the line be L1 and L2 having points (x1 ,y1 ) and (x2 ,y2 ) and locus of the geometric place of…

Q: Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0).…

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Q: 4:x 3+6r, y =-2+9t,: =1-12t and L:x=-1+4t, y 3+6,-8r

A: We are given L1: x=3+6t, y=-2+9t, z=1-12t. So, L1: x-36=y+29=z-1-12. Thus, a1=6, b1=9, c1=-12. We…