b. Find the component of B in the direction perpendicular to the plane ntaining A and C. (Hint: the component of a vector in a particular direction can found by taking the dot product of the vector with a unit vector in that direction.) C. Find the angle between A and B.

Q: The unit vector which is perpendicular to both r1=8ax+3ay- 2az , r2=2ax+7ay-6az is equal to

A: Given, vectors arer1=8ax+3ay-2az, r2=2ax+7ay-6azThe unit vector perpendicular to both vectorsr1, r2…

Q: Find the magnitude and direction of the vector. 75 mi W+ 180 mi a. 195 mi, 12° west of south b. 195…

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Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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Q: Given the vector u = 2i + 6j, find the magnitude and angle in which the vector points (measured…

A: Given :u=-2i+6j

Q: Find the angle θ between the vectors (a) in radians and (b) in degrees.

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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: Determine the dot product of vectors a, b when |a| = 5, |b| = 1 and the angle between a and b is…

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Q: Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find…

A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

Q: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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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: Determine the angles made by the vector V = (-59)i + (11) j with the positive y-axis. 169.44° O…

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Q: Given the vector u = (6, - 6), find the magnitude and angle in which the vector points (measured…

A: u = (6,-6)   Magnitude of u = ||u|| = √(36+36) = 6√2

Q: Find the unit vectors that are perpendicular to U = and V =,

A: Given the vectors U→=2, 3, 4 and  V→=-1, 3, -5 We will find the unit vectors that are perpendicular…

Q: Consider the figure below. If AABC is translated using the vector (r, y) → (1- 3, y+3), then rotated…

A: Identify the coordinate of C: The coordinate of C is: C-4, 1

Q: Use the cross product u ✕ v to find the obtuse angle between vectors u and v, where u = −i + 6j +…

A: The answer is in step 2.

Q: Find the angle between the vectors u = 2i +j+9k, v = 6i – 12j and sketch the vectors and the angle…

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Q: Given the vector u = (- 5, - 6), find the magnitude and angle in which the vector points (measured…

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Q: Assume vector V is in standard position, has the given magnitude, and that 0 is the angle V makes…

A:

Q: 14. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

A: Given V and W make any equal angle with L. |v| = |w| Z and L are orthogonal to each other.

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: 16. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

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Q: c) What is the cosine of the angle between the planes x + 2y – z + 1 = 0, and -x+ 3z + 1= 0? d) Find…

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

Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

A: Given points are P(2, 7) and Q(6, 4).

Q: Suppose a • b = -12 and b is a unit vector. a Explain why a and b are not perpendicular. b Given…

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Q: Find the x-component of this vector: 47.3 m 39.4° Remember, angles are measured from the +x axis.…

A: To find:- x and y components of given vector in figure

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

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Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: find the compoment form of vector v given ||v|| = 13 and the angle with positive axis is theta=300…

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Q: 3. Calculate the angle (degrees), between vectors p = 2i +9j – 4k and q = -3i + 5j + 6k correct to…

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Q: Assume vector V is in standard position, has the given magnitude, and that u is the angle Vmakes…

A: Given: Magnitude |V|=8.5 Angle θ=97°

Q: For what value of m, the vector 4i + 2j – 3k and mi – j + V3 k have same magnitude?

A: Given Data: Vector 1: x1i+x2j+x3k=4i+2j-3k Vector 2: y1i+y2j+y3k=mi-j+3k The magnitude of vector 1…

Q: |미350, | w|= 12, 0=35° A) B) W W

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Q: 4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east b. 12 N…

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Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

A: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

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Q: Consider the following three vectors, described here by their lengths and angles with respect to the…

A: The diagram below represents the vectors A→,B→, and C→ on the cartesian plane  (a) Consider the…

Q: Given the vector vec u = langle-6,-3 rangle , find the magnitude and angle in which the vector…

A: magnitude of x =x2+y2

Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: B side of cube = 10 cm (A. B); (C. D); (E.G);(G.B) ? (Ex F); (A x G) dan (Cx F) ? 2. what is the…

A: From the given figure we get A→ = 10i+10k B→ =10iC→ =5j+10kD→=5i +10kE→ =10i+10jF→=10kG→=10i+10j+10k…

Q: The angle between the vectors ū = i + 2j – 4k and w = 2î + 3j + 5k is obtuse.

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Q: Assume vector V is in standard position, has the given magnitude, and that u is the angle Vmakes…

A: The vector representation of of vector v with magnitude |v| and the angle θ, made by v with positive…

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: Find the value of a in the vector i = (a, b) if b = 48 and ||ū|| = 50 %3D v is in Quadrant I

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

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Q: Find the value of a so that vectors U = ai + 12j and V = 31 + 9j are perpendicular. a =

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Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

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Q: Find the angle a between the vectors L3] and]

A: Find the angle between vector s

Q: Suppose that |u| = 6 and |v| = 9, and that u times v = -37. Find the angle θ between the vectors u…

A: Vector Question

Q: Use the dot product to find the angle between the position vectors A and B.

A: Given: