4. If Ā = 5i+ 4j + 2k, B = 4i- Sj + 3k, and C = 2i-j- 2k, where i, j, k, are the unit vectors, determine (i) the value of Ā.B and the angle between the vectors A and B. (ii) the magnitude and the direction cosines of the product vector (AX B) and also the angle which this product vector makes with the vector C.

Q: Find the two values of t that would make the angle between vectors ⟨1, −2, 0⟩ and ⟨0, −1, t⟩ equal…

A:

Q: The vector from the origin to point A is given as (-2, 3, 5) and the unit vector directed from the…

A: A = (-2, 3, 5)  Thus, position vector of A,  a =  -2ax + 3ay + 5az   UB  =  0.535ax + 0.802ay -…

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: The angle 0 between the vectors u and v satisfies cos 0 So if u and v are perpendicular, then u'v =…

A: Given, the vectors u = (4, 5, 6) and v = (3, 0, -2). We have to find the angle between two vectors u…

Q: If the position vectors of P and Q are i + 3j- 7k and 5i- 2j+ 4k respectively, find PQ and determine…

A: The equation of the line, PQ passing through the points P and Q is defined as follows.…

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

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

Q: 5. Determine the resultant of two vectors with magnitudes of 30 and 70 units and an angle of 45…

A:

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

A: a)a→=-3 i + 8 jUnit vector as the same direction;u= a→a→ =(-3 i + 8 j)(-3)2+(8)2u=(-3 i + 8…

Q: 4 3 Let U 4 and V = - 5 - 3 -2. Find the angle between the vectors (in radians).

A:

Q: This question relates to three vectors defined as p = j- 3k, q =-2i -j- 3k and r= 4i +j+ 3k, where…

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Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

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Q: 1. The two unit vectors parallel to the line y = x- 3 are and

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the measure of the angle between the two vectors. 1) u = (4, 9) v=(-3, -8) 2) u = (-8, 9) v =…

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Q: The angle between two vectors a = (1, 1, 2) and b = (-1, 2, k) is 60°. Find the value(s) of

A: Topic:- application of vector algebra

Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

A:

Q: The inner(dot) product of two vectors and with lengths a and b. is given by a-b = abcos(y+2 T) ,…

A: The statement is true. The given statement is true because , Given a→.b→=abcosγ+2π But, cos…

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

A:

Q: The angle between the two vectors u = (4, 7) and v = (11 /2, 3 /2) computed via the cosine formula…

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Q: Find the vector v that has magnitude 3| and makes the angle 0 = n with the positive x-axis. v = help…

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Q: Find the angle between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Let u =⟨2,2,1⟩which makes an angle of 30∘ with v. If the dot product of vector u and v is 6. What is…

A: Given:   To determine: The magnitude of vector v

Q: 7. Let u and v be two vectors for which ||u||² + ||v||² = ||u + v||² From this information alone,…

A: Given that u2+||v||2=||u+v||2 consider the right hand side of the given equation. ||u+v||2=u+v.u+v

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: Find all unit vectors perpendicular to (3, 1, 4) that make equal angles withj and k.

A: Here we have to find the unit vector. The solution is following.

Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: What is the size of the angle between the vectors a = (2, 5, -1) and b = (-3, 2, 6)?

A: Given  a = (2, 5, -1) and b = (-3, 2, 6) To find angle between two vectors:

Q: Find the angle between vectors v = (1,2,3) and w = (2 -1, 4)

A:

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: If u = 2i -j- 3k, w = 3i – 9j+ 5k and v = perpendicular. 15i – 3j – 5k, then the vectors are Select…

A: which option?

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: If A = Si+ 4j + 2k, B = 4i- 5j + 3k, and C= 2i-j- 2k, where i,, k, are the unit vectors, determine…

A: Vector: A quantity that has both magnitude and direction is called a vector. Direction Cosines: If…

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: The angle between vectors A = 91-j+5k and B = (-2,7,1) is.. ******

A: According to our terms and conditions,we can only solve one problem at a time. So please repost the…

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: Find the measure of the angle between the two vectors. 24) u-(9,9) v-(-8,-5) V =

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Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: Find the angle between the vectors  [ 2 ]    And    [4] [ 1 ]               [6]

A: