(i) Find the direction cosines for v = 2, 3, 4 .  (ii) Verify that the sum of their squares equals 1.

Q: Express the vector in terms of it's length and direction. i + 2j - k

A: Solution:Given   i+2j+kTo express in terms of its length and direction.u=vvand v=vu

Q: Find the angle (in radians) between the 2 vectors U(-3, 4, -4) and V(1, 2, 2)

A: Given vectors are,               U(-3, 4,-4 ) and V(1, 2, 2 )

Q: The vectors a, b and c have been graphed below. Plot the result of a + b+c on the same axes. 3.

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Q: PQRS is a parallelogram and X is on the side QR. If vector PQ=3i+j, and  vector XQ=2i+j. find PX.

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Q: Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+ 4j-k

A: Simply take the dot/scalar product of both vectors a & b.

Q: Find the angle θ between the two vectors.

A: Now,

Q: Record the magnitude and angle of the vector sum.

A: Concept - first find the sum of x direction components and you direction components.

Q: 9. Illustrate how you would find the unit vector having the same direction as vector (p.q.r).

A: Formula: The unit vector in the same direction of a vector v→ is given by, v^=v→v Given: p, q, r To…

Q: On the diagram to the right, what are the components of the resultant of the three vectors shown? *…

A: We have three vectors, two of them are in horizontal direction, 6 N is -x direction and  14 N in +x…

Q: (a) Find the vector of length 2 that makes an angle of π/4 with the positive x-axis. (b) Find the…

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Q: Vector a is expressed in magnitude and direction form as a = (V30, 110°). What is the component form…

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Q: Find the angle e between the vectors. f(x) = 2x, 9(x) = 4x2, (f, 9) = radians

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Q: Find the angle 0 between the vectors. u = ( cos sin 4 V = ( cos sin 3 4 radians

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Q: The directional derivative at (xo, yo) is known to be 2 when the unit vector makes an angle of 30°…

A: Given Information - The directional derivative at x0,y0 is 2 when the unit vector makes an angle of…

Q: Use the formulas that we went over in the lecture to convert the following vector into "rectangular…

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Q: For the pair of vectors find 2U-3V

A: U=6, 6V=6, -62U=26, 6      =2×6, 2×6      =12, 12

Q: Find the angle 0 between the vectors. u = ( cos sin 4 v = ( cos sin 4 6 6. X radians

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Q: Explain how you might use the dot product of cos(B – a). two vectors to derive a formula for…

A: Here the objective is to derive the formula for Using the dot product of two vectors.

Q: Q4: using scalar prodect to find the angle between A= 2i+3j+1k B= -4i+2j-1k

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Q: find the component form of the vector. The unit vector that makes an angle u = 2π/3 with the…

A: Given vector is unit vector. So, magnitude v=1 Angle made by vector with positive x-axis is u=2π3

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle 0 between the vectors v and w.…

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

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Q: Find the angle 0 between the vectors. sin ). Зл v = ( cos 3N sin . 4 u = ( cos 6 4 = radians

A: Given,            u = cosπ6, sinπ6, v = cos3π4, sin3π4

Q: 6. The x-component of a vector is 4 and the y-component is -6. What is the magnitude and direction…

A: topic = vectors

Q: 4. A bullet is fired from ground level at a speed of 2200 feet per second at an angle of 30° from…

A: This is a problem related to vector components. Based on the general formula and concept we will…

Q: a = 3i - 2j + 5k and b = -2i-j+k, find 2a-3b and also its unit vector.

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Q: Find the angle 0 between the vectors. Зя sin 4 - (cos - sin 3 u cos

A: see below explanation

Q: The directional derivative at (xo, Yo) is known to be 2 when the unit vector makes an angle of 30°…

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Q: Find the angle 0 between the vectors. 5T u-(cos , sin S), v-(cos, sin 4) = 4 4 3

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Q: Find the angle between the vectors a 0 = and b = 2i+j - 4k. 10i - j - 5k

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Q: Find the angle between the vectors r = (-1, 2) and s = (4, 2)

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Q: Find the angle between u=3i+2j and v=-4i

A: Given,          The two vectors are u=3i+2j and v=-4i.

Q: Ã = ë, + 3ểy – 2ể, : Calculate the angle between the B = 4ëx – ëy : vectors A* and B". = -3e, - 5ẽ,

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Q: ind the angle between the vectors  [ 1 ]    And   [ -3 ] [ 3 ]             [ 2 ] [ 2 ]…

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Q: Find the angle between the vectors. (First, find an exact expression and then approximate to the…

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Q: find the component form of the vector. The vector 2 units long in the direction 4i - j

A: Given vector is u = 4i – j. So, the unit vector in the direction of the given vector is

Q: Find the angle e between the vectors. -(cos , sin 2), v- (cos , sin. x radians

A: Given that, u=cos3π4,sin3π4 and v=cosπ6,sinπ6. It is known that, the formula for u·v=u·v·cosθ.…

Q: Find the angle between the vectors ā = and b = . [Nearest degrees]

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Q: Find the angle between the vectorså = (4, 3) and b = (2, –1). (First find an exact expression and…

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Q: Find the angle 0 (in radians) between the vectors. sin + sin u = cos 4 v = cos 4 + sin 4

A: Trigonometry used:

Q: Find the angle 0 between the vectors. 3x, g(x) = x, (f, g) = (x)g(x) dx %3D !! radians

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Q: Express the vectors in terms of their lengths anddirections. √2i + √2j

A: If a vector is defined as: v→=ai+bj Then, the length or magnitude of the vector is: |v→|=a2+b2 The…

Q: Find the angle θ between the two vectors.

A: We need to find the angle θ between the two vectors.

Q: Find all points of intersection of the graphs of the two equations y = x2,          y = x1/3, (a)…

A: Note there are many subparts in the questions. So I will answer first two from the questions Given:…

Q: Find a unit vector in the same direction as (2i - 6j - k). Oi-j-k O

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Q: Determine the angle that the vector [- /3, – 1] makes with the positive horizontal X - axis

A: To find the angle between the vector -3,-1 and positive x-axis

Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). %3D cos-(금) O b. cos-) c. cos) O d.…

A: We need to find the angle between the vectors a=(3,4,0) and b=(4,4,2) We know a·b=|a||b|cos(θ) here…

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

A: