9. A rectangle is formed in R² by the vectors OA = (1, 3) and OB = (6, –1). a) Calculate the coordinates of the vertex C. А(1, 3) O (0, 0) b) Determine |OÁ| and |OB|. B(6, - 1) c) Determine its area.

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

A:

Q: Q4 find the length for the following vectors :- a) 2i + j - 2k b) 3i - 6j + 2k c) i +4j - 8k d) 9i -…

A:

Q: 4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5.…

A:

Q: 2.) Wrile pach vector below of the vectors in s.Cif possible), 0s a linear combination 5=d…

A:

Q: the vectors î+ cos - cos (ß- α) } + cos (y - α) k, cos (a − B) i + j + cos (y – B) k i + cos (B-y)…

A:

Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: Q3) A) Let 4 (-1 3, 4) and B (-5, 8, 10) two points in the space, find: 1- The vector AB. 2- Length…

A:

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

A:

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

A:

Q: 18. Find the projection of (0,4) onto (3,7).

A: Answer

Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

A:

Q: Find the vector in component form with initial poi

A:

Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

A:

Q: Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -1], v= [3 -1 -2] and w=[-2 2…

A:

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: 4. Express PQ-RO+SR-PS+RS as a single vector.

A:

Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A:

Q: 1) (10 points) Let a = -1i+2 + 2k and b = 2i − j + k. a) (3 points) Find a b b) (3 points) Find the…

A: a. The dot product of vectors a and b is -2.b. The angle between vectors a and b is approximately…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Let a and b be vectors in R?. (a.) Derive the area(2b + 5a, b – 2a) in terms of area(a, b). Explain…

A: Given: a,b∈ℝ2 If a=a1,a2 and b=b1,b2 then areaa,b=a1b2-a2b1. To do: Express the area2b+5a,b-2a in…