3. The position vectors of the points A, B and C are a = 3i – j- k, b= 2i+ 2j + 7k and c= 5i +2j – 3k. Find (i) the position vector of the centroid of A, B and C. (ii) the position vectors of the points P and Q which divide AB internally and externally in the ratios AP : PB =1: 2 and AQ : QB = –2 : 1.

Q: Consider the position vectors @ = 1î −3ĵ+2k and b = −1î÷2ĵ– 2 k. (i) Find the lengths of a and b.…

A: The question asks you to find several things related to the position vectors a and b:(i) Find the…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: Find the angle between the vectors 8i + 9j + 10k and 6i + 11j + 12k. ... The angle between 8i + 9j +…

A: Given that: vectors are: 8i+9j+10k and 6i+11j+12k

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: We have the following vectors: A = 2i - 2j + 3k, B=- -2i + 6j - 2k, C= -4i - 2j + k. Determine: a)…

A:

Q: Consider the three displacement vectors A = (4î - 3j) m, B = (2î - 5j) m, and C = (-3î + 5j) m. Use…

A: Component Method: For vector x=a i+ b j Magnitude is |x|=a2+b2 Direction is θ=tan-1(ba)

Q: (a) Find the area of the triangle with adjacent sides representing the vectors 2i – j + 3k, and i+…

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Q: If R =[E , F] ,Q =[F , C], Z = [D , B]. (a) Find the algebraic displacement vectors. (b) Determine…

A: (a) Algebraic displacement vector for points x1,y1 and x2,y2 can be written as follows:

Q: Consider the vectors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are…

A: Given vectors a = 6i + 7j + 6k and                        b = 4i − j + 8k, where i, j, and k are…

Q: The position vectors of the points A, B and C are a = 3i -j-k, b= 2i + 2j + 7k and e= 5i + 2j - 3k.…

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