Using coordinate geometry, prove the following case of the Crossbar Theorem, which is one result tacitly assumed in Euclid’s Elements but not stated

Q: Line L has the equation (2,-2,0) + t (2,2,2) Sphere S is centered at origin (O) with equation…

A: Given that: The equation of line L is L:r=(2,-2,0)+t(2,2,2). Sphere S is centered at origin (O) with…

Q: two vectors u = [5,4, -3], v = [1, -2, -1] form an angle θ that can be less than 90 ° (acute),…

A:

Q: The Critial Points of fcx,y)t+Ý-4y subject to the x+y=9 is O (o,さ3), (は5,2) ④ (e, さ)さ何,) None of…

A:

Q: Use spherical coordinate to evaluate V1² + y? + z² dz dy dr.

A:

Q: A variable plane lx+my+nz = p (where l, m, n are direction cosines of normal) axes at points A, B…

A:

Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

A:

Q: 4! find lim, B4,-2) S x approachesto I from postve direction.

A:

Q: After a reflection, the preimage A(2, 0) is transformed to the image A'(-2, 0). What was the line of…

A: As we know that, reflection of a point (x, y) in y-axis is (-x, y). So, the point (2,0) is when…

Q: b) Consider the vectors a = 3i – 2 j +7 K, and b = -5 i +4 j-3 k, find 1- a.b 2- Angle between a and…

A: b Given vectors are a=3i−2j+7k and b=−5i+4j−3k. 1 We have to find the a⋅b…

Q: All points with coordinates x= rcos(0) and y = sin(0), where r is a constant, lie on a circle with…

A:

Q: 1. Given the vectors Q = (3, - 2,-1) and R= (2,4,3), determine a) The projection of Q along R. b)…

A: Solution: The objective is to find the smallest angle of the given vectors

Q: Find angle = [0,] between the lines z = 2 + 3t, y=4-t, z=3+2t and x=1-8,y=5+28, z=6+38. Lütfen…

A: The angle between the lines x=2+3t,y=4-t,z=3+2t and x=1-s,y=5+2s,z=6+3s is to be determined.

Q: 3. u=8, |v|=3 and the angle between them is 125°. Determine b) the angle that u-v makes with vector…

A:

Q: Let A = (-1, 6), B = (1, 0), and C = (10, 3). Prove that AABC is a right-angled triangle. Let u =…

A:

Q: 45. In AXYZ, W is between Y and Z. The coordinates are X(2,3), Y(5,0), Z(0,0) and W (2,0). What is…

A:

Q: a) If Jä| = 2, JB| = 3 and the angle between å and b is, find the length of å- 2b. %3D %3D

A:

Q: Consider points A=(1,0,1) and B=(0,1,0) fasa and r [x+y=1 (==y+l and lines S: a) There exists C Er,…

A: By finding the equation of line passing through A and B, we can solve the question.

Q: 5) Determine the value of x. Assume that lines which appear to be tangent to the circle are tangent.…

A: According to the tangent theorm  Tangent to a point on circle are equal

Q: a) Draw the function y = sin=1 x (start the angle from –2n to 2t) b) Find a unit vector…

A:

Q: y U(a, b) V(?, ?) h =b units T(0, 0) a units W(c, 0)

A: HL congruence postulate: According to this congruence postulate, two right triangles are congruent…

Q: In the coordinate plane, Point B is 1 unit directly above Point A. When Points A and B are reflected…

A: Given that point B in coordinate plane is 1 unit directly above point A Points A and B are reflected…

Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Suppose v = (2, 5, 4), |w| = 3 and the angle between v and w is 30◦ (a) Find v · w (b) Find compvw…

A:

Q: Let w = (4,3, –1) and ở = (2,0, a). For which value of a is w orthogonal to u? Prove that there are…

A: vectors are orthogonal if their dot product is zero

Q: ) Prove that r1 and r2 intersect and calculate their intersection B) What is the angle between r1…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.