Q1) Given vectors (A = a, + a,) and (B = 2a, - 2a, - a,), when A is defined by Q (1,1,1) find (i) A × B (ii) The vector component of A at Q parallel to the line x-1, y=1 (iii) The angle between A and B. %3D |

Q: a= b=

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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: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: Consider the points A(-3, 4, 2) and B (8,-1, 5). (a) (i) Find AB. () Find AB (ii) 2 1 A line L has…

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Q: Given two vectors P=a,-a, Q-2а, -а, ta, R=2a,+3a,+a, Determine: (a). (P+Q)x(P-Q) (b). Q.RxP (c)…

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Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the point functions t= d6i +(e-6); +(-€)4 and 40=(2+2-/it (5- €);t (1-56)4 Intersect. at which…

A: Given: Two vector functions as r1t=2ti+t2-6j+-13t3k and r2t=2+2ti+5-tj+1-5tk, To find: The…

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Find the B-coordinate vector fe

A: First multiply some constant with given coordinator polynomial and equal the vector p(t) and find…

Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). O a. cos Cos cos-() O d. cos-() Ос.

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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: Solve the DE with general solution   6m''-7m'+20m=0

A: We need to solve the DE with general solution 6m''-7m'+20m=0

Q: Let x and y be unit vectors. Find the value of (x-10y) (x+10y) (x - 10y) (x+10y) =

A: Given that 'x' and 'y' be the unit vectors. To find the value of

Q: (4) You are doing some calculations about a solar panel on the roof of a house as shown in the image…

A: Given: Let the given vectors are a→=-10, 0, 6=-10i^ + 0j^ +6k^b→=0, 4, 0=0i^ + 4j^ + 0k^s→=13, 23,…

Q: Find the unit vectors u and uz in the directions of v = (1,3) and w = Find unit vectors U, and U2…

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Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.