Q1. a ABCD is a parallelogram. The diagonals of the parallelogram intersect at O. = a and OB (a) Find, in terms of b, the vector DB. (1) (b) Find, in terms of a and b, the vector AB. (1) (c) Find, in terms of a and b, the vector AD. (1)

Q: Q1/A/ Let u=5i-j+k, v=j-5k, w =-15i+3j-3k. Which vectors, if any, are a) Perpendicular? b) Parallel?…

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Q: Which of the following vectors is parallel to the line 7x+ 14y = 20? %3D (-6,3) (8,-16) (2,4) 0.…

A: We first find the slope of the line using y=mx+b form

Q: For what values of b are the vectors and orthogonal?

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Q: The points P and Q have position vectors a + b and 3a – 2b respectively relative to the origin O.…

A: vectors

Q: Q3/B/ For what value of 2, the vectors 2i - j+ 2k and 3i + 22j are perpendicular?

A: We can use the concept of perpendicular vector their dot product is zero.

Q: Q8. Find å – b, given that d = 4i – 3j + 2k, b = 2i – 4k %3D Find the angle between the two vectors.

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Q: point for the vect

A: What point is the endpoint for the vector corresponding to T(x)?

Q: 4. Let Ā = -(1+ m)î + 7j – 5k ,B = xî + (6 + n)j – 2k and C = (8+ m)î – 2k , find the following:…

A: Given data is : A→=-1+mi+7j-5kB→=xi+6+nj-2kC→=8+mi-2k

Q: given the vector, PQ, whose initial point is P(-2,-5) and whose terminal point is Q(3,4) the…

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Q: Q2/ A) Knowing that A = 2i+mj+k & B¯ =5i + j+4k are perpendicular vectors. Find the value of m then…

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Q: Q2: Find the angle between the vectors à and b where a = i+ 2j – k and b = -i+j-2k.

A: The angle between two vectors A→ and B→ is calculated as, cosθ=A→.B→AB The given vectors are,…

Q: What angle does the line of intersection of the planes (x 2y + 3z 5 and 4x+y-2z-7 make with the…

A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

Q: Q1/A/ Let u=5i -j+k, v=j-5k, w=-15i+3j –3k. W Which vectors, if any, are a) Perpendicular? b)…

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Q: Obthe resulting parallelogram from the following two vectors that form non-parallel sides A = 3 + 2…

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Q: What is the area of the parallelogram formed using the vectors below as 2 sides of the…

A: First we will find out the vectors from the graphs ,

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 6x Find -dA, where R is the parallelogram enclosed by the lines 4x – 3y 6x – y = 0, 6x – y = 9, – 4x…

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Q: b) How do you tell if two vectors are perpendicular?

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Q: Q:2) Find a vector that is parallel to the line whose equation is 5x-4 4-2z = 3 - 6y = 7 5

A: The given problem is to find the vector that is parallel to given parametric line equation, we have…

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q1.If à = 2a, + 2a, – a, and B = 3ax + 2a, – 6a, are vectors, find (a) Ả · B (b) Ả× B (c) Angle…

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Q: For the pair of vectors, find 4U +3V. %3D

A: In a product of one vector with a scalar quantity, the scalar quantity is to be multiplied with all…

Q: Q3: A and B two vectors are perpendicular to the plane C: - A = 4i + 3j – k and B = 2i – 6j – 3k ,…

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Q: (a) For the vectors d = (2, p, 8) and b = (q, 4, 12), determine values of p and q so that the…

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Q: The points P and Q have position vectors a + b and 3a – 2b respectively relative to the origin O.…

A: Given OP→=a+b, OQ→=3a-2b

Q: 2. Given two non-parallel lines l1: r = 2+t, y = 4+t, z = 8, and l2: x = 3, y = 2 + t, z = 5+t, (a)…

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Q: Find the equation of the line that goes through the point A = (5, –3, –4) and is parallel to the…

A: Given that the line passes through the point A=5,-3,-4 and is parallel to the vector  v=-2,4,3 The…

Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

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Q: Q2: If u = 2i +4j- 5k and v= -4i-8j+ak, (1) For what value or values of a will the vectors u and v…

A: Given: Q2. u=2i+4j-5k and v=-4i-8j+ak. To find: (1) For what values or values of a will the vector u…

Q: Q3:1r the two vectors A= 31+2j+5k, and B=21- j+ 4k, they located in the x and y plane, find the…

A: To find The angle between the two vectors

Q: Given that å = i+ 53 -3k and b = 3ỉ – 23 +k are vectors in 3D. Find the value of ả x b and b xả…

A: Given; a→=i→+5j→-3k→, b→=3i→-2j→+k→

Q: Q2. Find the angle between the vectors and .

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Q: Which of the following pairs of vectors are perpendicular? 1 -/2 > and OA. V2 > and В. - 2/2 > and…

A: If two vectors are perpendicular then multiplication of their direction ratio is zero.…

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: To determine the value of b for which the below vectors are orthogonal. −27,b,2, b,b2,b

Q: Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is…

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Q: Q3. Find the cross product of the vectors and .

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Q: Q1/A/ Let u=5i –j+k, v=j-5k, w =-15i+3j-3k. Which vectors, if any, are a) Perpendicular? b)…

A: find the dot product of u and v if the dot product is zero then vectors must be perpendicular. the…

Q: Given the two 3-D vectors a=[-3, 4, -6] and b=[-1, 2, -1], find the dot product and angle (degrees)…

A: Consider the given 3D vectors.

Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

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Q: Given vector A = 2а, + ба, За, and vector - B = – 3a, – 4a, – 5a,. Simplify the given mathematical…

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Q: For the vector r (3, - 1), what is -4r? The vector - 4r = ( ).

A: Given :   Vector r =  ⟨3, -1⟩  To find : -4r ?

Q: 2. Square ABCD is drawn as showWn below with the diagonals intersecting at E. a. State four pairs of…

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Q: Find an equation for the line through P(11,10) parallel to vector v=2i-3j

A: Given point on the line is P(11,10) The vector parallel to the line is,v=2i-3j

Q: Find the vector form of the equation of the line in R2 that passes through P= (2, - 1) and is…

A: If a line is parallel to another line, then they have same slope.

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: It is known that any two vectors are orthogonal if their dot product is zero. The given vectors are…

Q: Find the component form of the vector PQ, where P= (3,3) and Q = (5, - 8). The component form of PQ…

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Q: Find the vectors T, N, and B at the given point. r(t) ) =(2², ²32²³, t), (4,- 15, -2) N = B =

A: This question can be solved by applying the formula of T,N,B