Given three points, A(4, 3, 2), B(-2,0, 5), and C(7,-2, 1): (a) specify the vector A extending from the origin to point A; (b) give a unit vector extending from the origin toward the midpoint of line AB; (c) calculate the length of the perimeter of triangle ABC.

Q: 3) The lines I and m have vector equations r = (3i + 6j + k) + s(2i + 3j - k) and a) Determine…

A:

Q: iven the vectors a = (3,2,-1) and b = (1, -2,3), find the equation of the line joining a nd b. Show…

A: This is a problem of 3D geometry and calculus.

Q: For the given vectors: å = (-2,-3), 5 = (1,–2), 7 = (0,3), find: (a) 2å – 35 + ở (b) angle between…

A: Given the vectors a,b and c. The solution to the given questions are as follows.

Q: If la| = v2, la + b| = v6 and la – b| = v2, find the angle between the two vectors å and b.

A:

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)…

A:

Q: 8) An airplane is on a heading of 065° at 350 km/h and an 75 km/h wind is blowing from 310⁰.…

A: 0

Q: Take the two vectors: A = 3i + 4j C = 3i - 4k Let A and C be represented by arrows extending from…

A: b. A-C=(3i+4j)-(3i-4k)A-C=3i+4j-3i+4k=4j+4k

Q: Let be two vectors, such that a=(3î+2j-2k) cm and b=(2î+2ƒ+k) cm, calculate: (A) C²=3(a¹·b¹)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that the magnitude of vector u = 5 and the magnitude of vector v=7 and the dot product of u…

A:

Q: Find the angle between vectors: a = 51-4j+2k and, b= 41+3)+2√5k

A:

Q: 6) An airplane is on a heading of 020° at an airspeed of 600 km/h. A 75 km/h wind is blowing from a…

A:

Q: Vector A has a magnitude of 2.5 m/s at a direction of 18 degrees and Vector B has a magnitude of 4.5…

A: A) It is given that vector A  has a magnitude of 2.5 ms at a direction of 18° and vector B has a…

Q: ren vector A = -3î + 4j and B = i + 2j. Find vector V where magnitude is 3 and the vector is allel…

A: Parallel vector and magnitude is 3

Q: 1) Given two vectors as A = 2â, + 2â, -â, at point (3,60°,180°) and B =-2â, + 4â, - 4â, at point…

A: Consider the given vectors:

Q: The points A and B have position vectors such that OA = (3²) and OB = (2) The point G lies on the…

A:

Q: u = 57 - 5] + k and 7 = 27 + 14k.

A:

Q: 2) Express the resultant vector as a linear combination of unit vectors i and j and find the…

A:

Q: For the given vectors: å = (-3, –3), B = (1,–2), ở = (1,3), find: (a) 2å – 35 +ở (b) angle between…

A:

Q: For the given vectors: å = (-3,0), b = (1,2), ở = (1, -3), find: (a) 3å – 6+ 2č (b) angle between…

A:

Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…