15. Find in rectangular components the unit vector which is: (a) in the direction of E at P(2,3,-4) if E = (x² + y² +2²)(xa/√y² + z² + ya,/√√x² + z² + za₂/√x² + y²); (b) perpendicular to the plane passing through M(1,-5,5), N(-2,4,0), and Q(2,3,4), and having a positive x component. (c) Find the angle between the vectors RMN and RMQ-

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

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Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

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Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

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Q: A vector equation for the line through the points A (3, -4, -3) and B (3,4,2) is (x, y, z) = . (You…

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Q: 11. Let / be the intersection of the two planes 2x - 3y + 4z = 2 and x-z = 1 a. Find a vector…

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Q: 3. For the vectors b= (2, -1, -2) and a = (0, 4, –3) (a) Compute the projection of vector b onto the…

A: Consider the equation

Q: Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and…

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Q: 1. 3) Suppose A = 4i-6j, B = i + 7j and C = 9i - 5j. Find (a) ||5B-3C|| (b) unit vector having the…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: 2.30 Let r denote a position vector r = x= xê, (r² vector. Use index notation to show that: (a) ²…

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Q: 2. (6 marks) Find the vector equation of a plane a) Passing through the point A(-1, 2, -3) and…

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Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: i) If vector u and v are parallel or the same line, then Proj-u= (a) 1 (b) -1 (c) u (d) v (e) 0

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Q: CHCR) and C= Let B= - 3 of vis [v]B 1 1 [;)] 3 = A [v] 0 M-[2] 3 ⓇM1.- [³] B [v] = 0 0 4-A] -9 Ⓒ…

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Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

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Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

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Q: Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously…

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Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

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Q: 11) For u = (2,3,-1) and v (-1,01) find; %3D II a) proj,(u) b) The vector component of u orthogonal…

A: For finding projection using the formula, projv(u)=v→.u→v→2v→ The vector component of u orthogonal…