The direction angles of a nonzero vector a = (a1,a2,a3) are the angles a,ß, and y. a) Show that cos a² + cos ß² + cos y² = 1 b) If a vector has direction angles a =", and B =, find the third direction angle y.

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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Q: Prove the stated property of distance between vectors. d(u, v) = d(v, u) for all vectors u and v

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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: The solution is give as

Q: write the vector v in terms of i and j whose magnitude lvl and direction angle θ are given as lvl =…

A: For vector v, having magnitude v and direction angle θ can be represented in form of v = v cosθi^ +…

Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: The vector with length 4 and direction k is Di+Di+ j+ k.

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

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

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Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: Let a = (2, – 3) and b (0, – 3). - - Find the angle between the vector, in degrees.

A: Given a→=<2,-3>           b→=<0,-3>

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

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Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

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 that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

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: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

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Q: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: Let b be the vector of length 35 that when drawn in standard position makes a 290° angle with the…

A: Given : length of vector b=35 ⇒b=35 Also, b makes angle 290° with positive x axis. So, b=b1i+b2j,…

Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: If A=(rsinOcosð,-cos2OsinD, tan, Inr) at P(7,0.08 rad,4.66 rad), determine the vector component of A…

A: Given:

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: 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: Exercise 1:If 0 is the angle between vectors a and b, show that projab. projpa = (a.b) cos (0) COS

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Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: wich whose velocty vector is 301, assuming the the units Which is travelling faster, a car whese…

A:

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Verify the parallelogram law for vectors u and v in R": |u + v|l? + ||u – v||° = 2||u||? + 2||v||?

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Q: After decompsing the Veclor A-2i-j+3k to Hhe Sum of tado vectors, the first is Parallel to the…

A: Every vector can be decomposed into two vectors. One vector is parallel to another given vector, and…

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: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Verify that the vector i = ( ) is a unit vector (that is, has length 1). Then determine the…

A: The projection of a vector w in the direction of v is given by v·wv2v

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

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: Find the angle θ between the vectors.u = (3, 1), v = (−2, 4)

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

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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: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

A:

Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

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: An object with a mass of 10 kg is suspended from a ceiling by two lengths of rope that makes angles…

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Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…