10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k, OB = 3i + 2j + 3k and OĆ = i+j + k. %3D %3D (a) Using a scalar product, show that angle ABC is a right angle.

Q: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: 1.) Given the points M(0.1,–0.2,–0.1), N (-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: a.) the dot…

A: RMN = (-0.2, 0.1, 0.3) - (0.1, -0.2, -0.1)RMN = (-0.3, 0.3, 0.4)RMP = (0.4, 0, 0.1) - (0.1, -0.2,…

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

A:

Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

A: Given query is to find the equation of the line.

Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: In the figure, a vector a→ with a magnitude of 24.1 m is directed at angle θ = 68o counterclockwise…

A: Given that: Magnitude of a→ =24.1mAngle of a→ w.r.t. coordinate axes: θ=68°Angle of primed…

Q: 3) Find the angle between A = 2i + 2j – k and B = 6i – 3j + 2k. 4) Determine the unit vector…

A:

Q: 9. ABCDEF is a regular hexagon with centre O. FA = a and FB = b. %3D %3D Express the following…

A:

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OÁ = 2i + 5k,…

A: (a) Given that position Vectors, OA→=2i+5kOB→=3i+2j+3kOC→=i+j+k   As we know that, two vectors are…

Q: Find the measure of the smallest nonnegative angle between the two vectors. Round approximate…

A:

Q: Two vectors of magnitudes B= 5 and C = 3 are lying on the xy plane as shown in the figure. What is…

A:

Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: What angle does the line of intersection of the planes (x 2y + 3z 5 and 4x+y-2z-7 make with the…

A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

Q: nd the unit vector 3i - 4j+ 5k perpendicular to the vectors: 4i + 5j-6k

A: Let the given vectors be  u→=3i-4j+5kv→=4i+5j-6k we have to find the unit vector perpendicular to…

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…

A:

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Find the cross products u x v and vxu for the the vectors u

A:

Q: 4.18. Given vectors u = 3j – - 6k and v = 6i – 4j – 2k, find the dot product of u and v.

A:

Q: For a vector of my oriented at 245 degrees on the hexagonal system, find the projections of this…

A: We have to find the projection of the hexagonal system on the six leads.

Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

A:

Q: 15. Given the vector u (2i + 5j) and vector v = (3i + 4j), find the dot product u v %3D

A: We have to find the dot product of given vectors.

Q: 2 Let u = = 1 (i) Find the angle between u and v. (ii) Find a vector w of length 2 in the direction…

A:

Q: (B): Find the unit vector perpendicular to the vectors: 31-4/+5k ; 11+5/-6k dw (C): If w = tan x and…

A:

Q: 2. Consider the two vectors a and b, as graphed below. 2a Plot the result of a +b on the same axes.…

A:

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

A:

Q: Answer either A or B. A) Let V = 21 + 3j – k and W = -i - 5j – 6k, then find cos 0, where 0 is the…

A: Vector problem....

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: 2) Let u=5i-j+k, v=j-5k and w=-15i +3j-3k. Which vectors, if any, are: a. Perpendicular? b.…

A: To find out the vectors which are parallel and perpendicular.

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

A:

Q: The vectors v = (3, 4) is projected onto the x-axis The length of the projection is %3D A/

A: We have to find

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

A:

Q: The.vectors (2i - 3 j) , (3i – j) and (2k - i) are Parallel to each other Perpendicular to each…

A:

Q: Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular…

A:

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

A:

Q: 1. Find the angle between two vectors u = i-2j - 2k and v= 6i + 3j+2k.

A: Given two vectors u→=i-2j-2k and v→=6i+3j+2k. Here find the angle between two vectors.

Q: (b) Two out-of-phase alternating voltages are represented by: V = 3.4sin (wt +=) and V, 1.3cos (wt…

A: The given problem is to find the sum of given vectors in the form of A sin(wt+ ϕ),we have to general…

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

A:

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

A:

Q: A, B and C are points in space relative to 0 such that AB 1 CO and AC 1 BO. Prove that BC 1 AO. The…

A: Given: A, B and C are points in space relative to O such that AB⊥CO and AC⊥BO. To show: BC⊥AO.…

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

A:

Q: 22 Given the cross product of 2 vectors u and vis, u x v= -3i-3j+3k, and their dot product is,…

A:

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

A:

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: 8 Find the 3-dimensional unit vector in the direction: a 2i + 3k 6 -i+ 2j – k c 2i – 2j + k

A:

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

A:

Q: 8. In triangle ABC, the point D is the midpoint of BC and E the midpoint of AC Vectors are marked as…

A:

Q: If A = 3i + 4j and B = 7i + 24j, the %3D vector having the same magnitude as B and parallel to A is…

A:

Q: On: A IS tor while A is a scalar. |A|. If A B < 0, then the (smaller) angle between the vectors A…

A:

Q: 1) Suppose a and b are two vectors that start from the same initial point. If |a| = 8 and |b| = 11,…

A:

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.