(d) Three vectors are given by: P= 2i – k Q = 2i – j + 2k R= 2i – 3j + k Determine: (i) (P + Q) × (P - Q); (ii) Q•R × P; and (iii) P•Q × R.

Q: Q3/B/ For what value of 2, the vectors 2i – j+ 2k and 3i + 21j are perpendicular?

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 14i V=-7i

A: To find Angle between two vector a→,b→ we use, cos α =  a→·b→|a→|·|b→|

Q: a vectors p = (2) and t = (,).

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Find cos(0) if 0 is the angle between the vectors u= 2i + 2j – k and v = 3i + 4k

A: Consider the two vectors. u=2i+2j-k and v=3i+4k It is given that θ is the angle between the vectors.…

Q: 7. i and y are vectors of magnitude 1 and 2, respectively, with an angle of 120° between them.…

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Q: a) Let a = 2i – 3j + xk and b = -3i + j + xk. Find the values of x for which vectors a and b are at…

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Q: Q3/B/ For what value of 2, the vectors 2i - j+ 2k and 3i + 22j are perpendicular?

A: We can use the concept of perpendicular vector their dot product is zero.

Q: 5. For the vectors = (-3, –4) and v = (-2, 2) Find the dot product u · v, and the angle 0 between…

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Q: 19 Use the given vectors to find V.w and V-V V= 6i-25, w=-4i-3

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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: 2. The two unit vectors parallel to the line 3x + 4y = 1 are and 3. The two unit vectors…

A: 2) The line is 3x+4y=1. Rewrite the equation of the line in the slope intercept form as,…

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

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

Q: 8. If you know that the vectors a = 4i-j + 2k and b =4i-2j-5k, then the lengthvector %3D a - 2b = A.…

A: To find: The length of the vector a→-2b→. Given: The vectors are a→=4i-j+2k and b→=4i-2j-5k. Concept…

Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: snip

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Q: Find cos(0) if 0 is the angle between the vectors u = 4i – 3k and v = 2i – 2j + k

A: Given,           u=4i+3k           v=2i-2j+k

Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)

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Q: (3) For what value(s) of a will the vectors u = 2i + 4j-5k and v= -4i-8j + ak be parallel? V ا ) وہ…

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Q: 21A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, and C = i-2j+ k, find (A x B).C

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Q: Q2: Find the angle between the two vectors A = 5i - j+ 2k and B = -3i + 2j + k

A: Angle between the vector u and v is θ=cos-1u.vu.v.

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: 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: Q.3 Find the cosine of the angle between the vectors: a = 2i-8j + 3k a =i+2j-k a = 4i + 2j-k b= 4j +…

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Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: Q1. Consider the vectors A =4ax+2kay+kaz and B = 4ax+4ay-4az what value of k the two vectors. B will…

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Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

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Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

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

A: Given That: The unit vector is perpendicular to r1=8ax+3ay-2az & r2=2ax+7ay-6az

Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: A=4+J1 and B=2+j3 respectively determine the sum and the difference of the vectors in both…

A: Concept: Complex numbers: Complex numbers are two-dimensional complex or s-plane points that are…

Q: Q3 find 1)angle between two vector. 2)projection of vector A&B. A = 2i + 2j - K B = 4i-6j + 4k

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Q: 1. The two unit vectors parallel to the line y = 2x 1 are | and 2. The two unit vectors parallel to…

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Q: 1 -E---Fl 2 V2 = 0 , and v3 = -5 span R³? Why or why not? 3 Do the vectors V₁ = -31

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Q: Q3/A/ If ā = i – 2j + k , Find: i) (ā x b). (ā x c) ii) (ā × 5) × (ā x c) tho vectors 2i - i+ 2k and…

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Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: 1. The two unit vectors parallel to the line y 5x + 2 are and 2. The two unit vectors parallel to…

A: 1. Put x=t, then y=5t+2 and the parametric equation of the line is rt=t,5t+2=0,2+t1,5 and parallel…

Q: 41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

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Q: %3D 2a+3b+4c = ( 3. 2. =q C. 3. 4 Vectors

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Q: Using a convenient scale, find the resultant of the following vectors graphically: 10m at 40o with…

A: According to Polygon Law of forces, if a number of coplanar forces acing at a point is represented…

Q: Q.2 For the twa Vectors A i-3 -2k B = 3i +šj +7K

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Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k 41 +5/-6k i (C): If w = tan x and…

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Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

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Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

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Q: Q3/the parallelogram is determined but the vectors KL = and KN =, so the area of parallelogram KLMN…

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Q: Q3: Find the angle between two vectors in space A = 41 - 2J-k B = 4T - 2J + 4k and

A: We need to find the angle between vectors A=4i¯-2j¯-k¯  and B=4i¯-2j¯+4k¯ for this we will use the…

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^