Draw AABC and label the midpoints of AB, AC, and BC as X, Y, and Z. respectively. Let P be the midpoint of BZ and Q be the midpoint of Cz. Prove that PX = QY.

Q: Where M, N, and P are the midpoints of the sides of  triangle RST and C is the centroid of the…

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Q: Find the coordinates of W. When point W lies on UV such that UV:VW is 5:2

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Q: Given =16,-2,k) and V=14,-4, 0]. Determine the value(s) of k if the angle between ü and v is 60°.

A: We will find the possible values of K as shown below

Q: Every triangle has a balancing point, called the centroid. O True O False

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Q: LG, CF, and AU are concurrent.

A: According to the question, To show that LG, CF, and AU are concurrent, we will use the theorem…

Q: If p = 2i +j - kand q  = i - 3j +2kdetermine the norm of the addition of p and q, and the magnitude.

A: Consider the given information. p=2i+j-kq=i-3j+2k Find the sum of p and q. p+q=2i+j-k+i-3j+2k=3i-j+k

Q: Find the projection of y onto v. Find the distance between y and v. y = 1 2 -3 1 , V = 1 1

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Q: Find u · v, where 0 is the angle between u and v. ||u|| = 4, ||v || = 64, 0 4

A: Directly use the formula for dot product of two vector and simplify the result.

Q: Let A = (1, 1, -1), B = (-3, 2, -2), and C = (2, 2, -4). Prove that ABC is a right-angled triangle.…

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Q: let R = (1, 4, 3). RÓ has components (4, 1, 1), and Find the point Q such that v = sketch v.

A: Given: The components of vector v=RQ⇀ and  R= (1,4,3)  To find  Q and sketch v

Q: Find the dot product v*w and the angle between v and w. v = i + j, w =i + j - k

A: Given: v=i+jw=i+j-k To Find: The dot product of vector v and w and the angle between v and w.

Q: Find the projection of v

A: Here v→=2i^-2j^    and w→=-3i^+j^

Q: Let v = (a, b, c). Calculate v × i, v × j, and v × k.

A: given: v=a,b,c we have to calculate v×i, v×j and v×k

Q: Find the length and direction (when defined) of u x v. When : u = 2i +2j -k; v = -i + k;

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Q: 18. Show by vector methods that the median (a median joins the vertex of a triangle to the midpoint…

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Q: In the below triangle, C is the centroid and KG, LF, and JH are all medians. If FC-2, find CL and…

A: We know that the centroid divides the median in 2:1 ratio. So, CLFC=21or, CL2=2or, CL=4So,…

Q: ā − Let a = and b = . - Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A: Let .To find  will be orthogonal.

Q: Let u=i+j, v=j and w=k. Find c₁, c₂ and c3 such that 5i +5j + 4k =q₁u+c₂v+C₂W.

A: Given: u=i+j  v=j  w=k