1. Let u and v (a) Draw u and v in R. (b) Use the parallelogram law to add 2u - v to your picture. (e) Calculate 2u - v and verify it coincides with your sketch in part (b). (d) What is Span(u, v)?

Q: 2. a (-9,6) and b =(3, 1). What is the component form of the resultant vector tor/a - 26 ?

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Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

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Q: Illustrate how you would find the unit vector having the same direction as vector (p.q.r).

A: Given vector is p,q,r. We have to illustrate the method to find the unit vector having same…

Q: 2. Find the angle between vector [2, -5,7] and vector [6,4,1]

A: Vector [2,-5,7] and vector [6,4,1]  We have to find angle between these two vectors

Q: 5. a) What is the orthogonal projection ŷ, of y = 1 = ( ² ) U = and the origin? -3 9 onto the line…

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Q: Let u = (2, -3, 4) and v = (-2, 1, 3). What is the dot product u v? What is the angle between u an v…

A: The given vectors  and

Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: 3. Consider the following vectors: (2,3) & (-5,1) a. Find the dot product between them b. Find the…

A: We have to find the dot product and angle between two vectors.

Q: Write a vector equation and parametric equations for each line. a) 3x - y = 7

A: note : as per company guidelines we support one question in one request. kindly repost next question…

Q: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: You know that vectors show not only magnitudes, but directions as well. Explain how vector functions…

A: we know that vectors show not only magnitudes, but direction as well. we have to explain how vector…

Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

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Q: 1. Use components to find the magnitude and direction of a) Ã + B; b) Ã – B; c) B – Ã. Ã (2.80 cm)…

A: a) The magnitude of given vectors are A→=2.80cmB→=1.90cm The X and Y components of  A→ are…

Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: (c) Use vector methods to find the point P on the circle (x - 5)² + (y-4)² = 4 which is closest to…

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Q: draw a set of x-,y-, z- and axes and plot the following position vectors (including rectangular…

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Q: 1. (a) Find uxv and show that it is orthogonal to both u and v u = v = (b)The vertices of a…

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Q: Find parametric equations for the line through Po = (10,-1, 1) perpendicular to the plane 2x + 3y -…

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