5. Add vectors 2i– 2j & i+5j by a) Graphing these two vectors in a coordinate system in standard position. (Use graph paper if you have it.) b) Add the vectors components and find the resultant. Graph the resultant. c) Redraw the vector i+5j at the end of the first vector 2i – 2j. Does this agree with what you found as the resultant? Explain.

Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: B) Determine if the two vectors are orthogonal or parallel or not? A=6i + 6k and B--2i +2j+2k

A: We have to check that the two vectors A→ and B→ are orthogonal or parallel. So, we find the angle…

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: Write three properties of parallel vectors p and q.

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: 2. Add the vectors by rearranging them and then sketching the resultant. u W a. Add the vectors by…

A: To add the vectors  we should sketch the x-y plane .

Q: unit

A: To get the unit vector that is in the same direction as the original vector v, we divide the vector…

Q: 1. Given two vectors P= ai+ bi + ck where a, b,c represent the last three digits of your index…

A: According to question vector's will be, P→=ai+bj+ck=0i+2j+8kQ→=-3i-5j+4k i) Dot product between…

Q: Find the resultant using (a) the parallelogram method, and (b) by summing up components. For the…

A:

Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

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: 5. Determine the resultant of two vectors with magnitudes of 30 and 70 units and an angle of 45…

A:

Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

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: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

A:

Q: Give vectors a, b, c, d such that a=5c + 3d and b= 2c - d express 2a - 3b in terms of c and d

A: Solution as given below:

Q: A unit cube (whose length, width, and height are 1 unit each) with a vertex at the origin lies in…

A: Given, cube is-

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: Find the resultant of the vectors A and B. Ả = A = 8a, + 7ay + 2a, B = -Зах — 8ау — ба, Draw the…

A:

Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

A:

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: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

A:

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

A:

Q: 2. Draw a figure to illustrate part of the infinite pattern that can be derived from a given…

A: Given data is: Draw a figure to illustrate the part of infinite pattern that can derived from…

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

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: What is the dot product of the vectors a = 4i + 3j and b = -3i + 4j?

A: Solution is given below:

Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

A:

Q: Given the vectors, a = (4,-5) and b = -10i -8j: %3D a. Find a - 2b.

A:

Q: Do the vectors A = 2ax +ay-4az, B =3ax %3D -2ay + az and C = ax -3ay +5az form a %3D right triangle?…

A:

Q: Show that each pair of vectors is perpendicular.     2i + j and i - 2j

A: Solution: Consider the given vectors are  a→ = 2i + jandb→ = i - 2j We know that if the dot product…

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: Express the vectors in terms of their lengths anddirections. 2i - 3j + 6k

A: The given vector is a=2i-3j+6k. Compute the length of the vector as follows. a=22+-32+62=4+9+36=49=7…

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 (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: 10,7 and -2,-75

Q: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. Enter the vector i as i,…

A: here here we have

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) If u and v are two-dimensional vectors, we calculate the dot product as   u=(u, u2) and v=(v1,…

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

A: Given:  i + 2j - k

Q: a-(:) We have two vectors: a = and b= What is the resultant of -a plus b? (

A:

Q: Determine if the given vectors in the picture are orthogonal, parallel or neither.     *Please go…

A:

Q: 4. Now, let's assume that A, B, C, and D from above are each the resultant of 2 component vectors (x…

A:

Q: b. Please provide a well explained answer for the follwoing. And explain how to add/subtract…

A: We have to write definition and some basic properties of vectors.

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

A: The given figure is:

Q: (b) Find the sum of the vectors 3î + 7ĵ – 5k, 2î – 3j – 8k and i- 2j + 12k. Also calculate the unit…

A:

Q: Perpendicular vectors are also said to be __________.

A: Perpendicular vectors are also said to be __________.

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.