(b) For any arbitrary vectors u, v and w, prove that (u x v) x w = u x (v x w) if and only if (u x w) × v = 0.

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Plane passing through the point (0,2,-3) and with normal vector 4i - j -2k means perpendicular to…

Q: Consider two vectors ā = 4i – 5j + 2k and b = -2i + 2j + 7k. Find (a) ä + b (b)ā – b, and () a thicd…

A: Given vectors are  a→ = 4i^-5j^+2k^b^ = -2i^+2j^+7k^

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: The result of (j x k) · (k x î) is

A: SOlution: To find the cross and dot product of given i vectors

Q: What is the scalar product A*B if A=Xi+Yj and B=Xi-Yj?

A: Given data: Two vectors A→ = Xi^+Yj^B→ = Xi^-Yj^ Required: The scalar product

Q: Dot Product, polar coordinates: If A = 8 < 21 degrees and B = 5 < 62 degrees, find А-В

A: We will first convert the polar coordinates into the cartesian coordinates. Using these coordinates…

Q: Consider the vectors A = (-5.4, 8.8) and B = (8.7, -9.4), such that A - B + 3.8C = 0   What is the x…

A: Let the coordinates for point C be (x, y).For the given coordinates of A and B, vector…

Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

A:

Q: Consider the vectors A = 6i + 3j and B = 3î - 6j.

A:

Q: For the vectors A=8.94i +6.93j-17.9k, B=7.67i-6.06j+10.2k, and C=6.25i-3.34j-9.61k, find C(A-B).

A: The difference vector between the two vectors is,

Q: / The vectors A and B are given by A=-2î –3j and B = i -2j. nd 1.AxB and verify thatAxB =-BxÃ. 2.…

A: Given values:- A→=-2i^-3j^ ----(1) B→=i^-2j^ ----(2) (1) Let (R→) be the resultant value of A→×B→…

Q: Problem 4: Consider the three vectors A = 2.3i + 2.1j+9.3k, B = -11.6i + 1.1j+ 4.1k, and C = 1li -…

A: solution as

Q: Th unit vector from the origin {i.e. the point (0,0)} to the point B (3,4) is:

A:

Q: Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }

A: To solve the given question, we will write down the given two vectors in vector form and then we…

Q: If the vectors 6i- 2j + 3k, 2i + 3j - 6k and 3i+ 6j- 2k form a triangle, then it is (a) Right angled…

A: Given vector--- vector P = 6i-2j+3k . vector Q = 2i+3j-6k . vector R = 3i+6j-2k . We have to…

Q: Show that for orthogonal coordinate systems gij= 0 for i not equal to j

A:

Q: Find the angle between the two vectors Ả = 2 î + 3ĵ + k B = -4 î + 2ĵ – k and

A: Given  A=2i+3j+k B=-4i+2j-k

Q: Two points are given in polar coordinates by (rθ) = (2.00 m, 50.0°) and (r,θ) = (5.00 m, −50.0°),…

A: Given: (r, θ) = (2.00 m, 50.0°) and (r, θ) = (5.00 m, −50.0°)

Q: Given two vectors A = 4.00 +7.00 and B=5.00 -2.00, find the vector product Ax B (expressed in unit…

A: Cross product: Cross vector of two vectors A→and B→ is given as, A→×B→=i^j^k^AxAyAzBxByBz where Ax,…

Q: What is the vector product of A = 2.00 i^ + 3.00 j^ + 1.00 k^ and B = 1.00 i^ - 3.00 j^ -2.00 k^?

A: The given vectors, A→=2.00 i^+3.00 j^+1.00 k^B→=1.00 i^-3.00 j^-2.00 k^

Q: Find the divergence and rotation of the following vector A=i(x^2+y^2)+j(y^2+zx)+k(z^2+xy)

A:

Q: Given vectors P=(3 m, 4 m) and Q=(4 m, 3 m), find the angle of P + Q.

A:

Q: Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from…

A: When subtracting vectors, the rule is to graph the first two from the origin and then connect them…

Q: Show that when A⃗ +B⃗ =C⃗ A→+B→=C→, then C2=A2+B2+2ABcosφC2=A2+B2+2ABcosφ, where φφ is the angle…

A: Given:-  A→+B→= C→ Find:-  Show that C2 = A2+B2+2ABcosφ here φ is the angle between vectors A→ and…

Q: Given these vectors: A = (0.9)î + (-9.8)ĵ+ (7.8)k B = (8.7)î + (0.2)ĵ+(-8.9)k | Find the value of…

A:

Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (5,…

A: Vertices of rectangle: A(5,6), B(8,12), C(-40,36), D(-43,30)  When we'll plot these vertices on…

Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: Which of the following is the conserved quantity if the system having Lagrangian L= = m(x² + y²) – ²…

A:

Q: 7.60 In Problem 7.59, what is the vector component of F parallel T to the surface?

A: As A is at the centre of the plane so, The coordinate of A will be half of the plane's coordinate:-…

Q: - Calculate that [x, y] and [P],

A: In quantum mechanics, position operater, x^ , y^ , z^momentum operator, p^x, p^y, p^zQuantum…

Q: Given M = 6 î + 5 j – 6 k and N = 3 î - 3 j – 3 k, calculate the vector product M x N.

A:

Q: Can two vectors, of unequal magnitude, add up to give the zerovector? Can three unequal vectors?…

A: If two vectors have equal magnitude but different directions then only their sum will be zero.

Q: prove that F(x, y, z) = (3x² + .

A: Solution:

Q: Let be two vectors, such that a=(3+2j-2k) cm and b=(2î+2j+k) cm, calculate: 1) The angle between the…

A:

Q: Find the scalar and vector projections of a and b if a = 3i − 3j + k and b = 2i + 4j

A:

Q: Given the two vectorsA=-8i,-4j,-6k and B=2i,+3j,-7k, find (a) A+B, (b)A-B, and (c)-4A (d)A•B (e)AxB…

A: Given:

Q: The vectors from the origin to the points A, B, and C are i + j, 3i + k, and 4i – 3j – 4k,…

A: We first find the vectors of the sides AB, BC and CA. Then find if any two vectors are perpendicular…

Q: Prove that a. V.E= L а. 0. b. V•B=0

A:

Q: What is the scalar and vector product of A and B respectively, if A =2.2 î+3.4 ĵ B=4.4 î+2.0 ĵ

A:

Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…

Q: 2)1F the Volume is egual to Zero ,then the all Vectors line in the same planc. a.T b.F

A: Given  volume of parallelepiped formed by the vectors is zero

Q: For the vectors i and v given below, find u i, the hermitian products u into i and i into u', the…

A: