a) Show that if v is any nonzero vector, then v is unit vector b) use the result in part (a) to find a unit vector that has the same direction as the vector v = (3,4). c) use the result in part (a) to find a unit vector that is the oppositely directed to the vector v = (-2,3, -6).

Q: Determine the two unit vectors that are orthogonal to A= . Which two unit vectors are parallel to A?

A: Given that, A = <1, 2> Suppose that <a, b> is orthogonal to the vector A = <1, 2>…

Q: C A

A: We use Triangle law

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

A:

Q: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

Q: Determine whether the vectors u = and v = are perpendicular.

A: As we know that if the dot product of two vctors is zero then we can say that the vectors are…

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: Find a non-zero vector perpendicular to the vectors and ú =

A:

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: If vector a= and vector b= are vectors a and b orthogonal, parallel, or neither? Provide

A:

Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v…

A:

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: It is asked to represent the given vector with initial point P and terminal point Q in component…

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: A VECTOR V WITH INITIAL POINT P(X1, Y1)  AND TERMINAL POINT Q(X2,Y2) IS GIVEN BY V = (X2-X1) i…

Q: Let the vector 3i +j can be expressed as a sum of vectors u and v where u is parallel to the vector…

A:

Q: Write the vector v = ⟨2, -4, 4⟩ as a product of its magnitude and a unit vector with the same…

A: Given vector is  v=2,-4,4 Magnitude of vector v  is v=(2)2+(-4)2+(4)2=4+16+16=36=6 Now, unit vector…

Q: A vector is in standard position if the _____ of the vector is placed at the ______ ofa rectangular…

A: To fill up the blanks,  A vector is in standard position if the _____ of the vector is placed at the…

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

Q: Prove that the points with position vectors a+2b, 2a−b and 3a−4b are collinear.

A: We have to use determinant method to solve.

Q: Determine the value(s) of ? such that the vectors [5, ?, −8 ] and [3, ?, ?] are perpendicular.

A:

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

A:

Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

A:

Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: Find a unit vector u in the direction opposite of (-8,-4,-3).

A:

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

A:

Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

A:

Q: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the…

A:

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: tind a non-zero vector perpendıcular to the vectar u. Find the length of the vector R-

A: Consider two vector u→=ai→+bj→ and v→=ci→+dj→ if the two vector is perpendicular then the angle…

Q: If vector a= and vector b= .. are vectors a and b orthogonal, parallel, or neither? Provide…

A: Topic = Vector   2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Determine if the vectors u=, *v= and w= lie in the same plane or not

A:

Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

A:

Q: Find the unit vector that has the same direction as vector v that begins at (0, -3) and ends at (4,…

A: If a vector is of the form ai^+bj^   then its unit vector along the direction v is written as…

Q: Find a unit vector u that had the same directions as the vector v= (-3,3,-2)

A: Use the basic property of unit vector

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar lul.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: u  Solution: Magnitude of a vector is…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

A:

Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

A:

Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

A:

Q: Consider

A: Please refer to the image below

Q: a b

A:

Q: find the component form of the vector. The unit vector obtained by rotating the vector [0, 1]…

A: Given unit vector is 0,1 makes an angle of 90°. The vector obtained by rotating it by 120° counter…

Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A:

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.