18. Show by vector methods that the median (a median joins the vertex of a triangle to the midpoint of the opposite side) drawn to the base of an isosceles triangle is Perpendicular to the base. Hint: Take A as origin and show that AM•BC = 0.

Q: 1. Find DATE: NO. the rector y with base at A and base at B from the information given. Draw a…

A: Step 1: Step 2: Step 3: Step 4:

Q: 1. Given the points P(5, 3, - 4) and Q(7 - 1, - 3), find the following: a. the vector PO b. PQl

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

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

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Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: Find the area of parallelogram with the vectors u = = (2, –2,0) and v = (0,–2,0) for sides.

A: The area of  parallelogram with vectors u=(2,-2,0)  and  v=(0,-2,0)  for sides is the cross product…

Q: 1. AB and CD are parallel and 15 centimeters apart, mZBAC = 58° and %3D is the reflection through AB…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. You can…

Q: Show that the lines L₁ : x = 1 -t, y = 2t, z = 5 + t and L₂: x=1+3t, y = 3-6t, z = 5-3t are parallel…

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Q: Find the lengths of triangle PQR. Is it a right triangle? Is the triangle equilateral, scalene, or…

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Q: Sketch the vector field in the plane along with its horizonta and Vertical a representative…

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Q: i) ii) Draw a vector diagram for the cyclist's trip. Find the distance covered by the cyclist. (Give…

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Q: In a regular hexagon ABCDEF point G is the midpoint of line segment EF, point S is the intersection…

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Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: Find the projection of v

A: Here v→=2i^-2j^    and w→=-3i^+j^

Q: ans ) Find the lengthaf the Projection of the line jeining (-1,2,) ane -19 2) on the Plane…

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Q: find the compoment form of vector v given ||v|| = 13 and the angle with positive axis is theta=300…

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Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

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Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…