Solve for the magnitude of the resultant and the direction cosines of the following cartesian vectors.  -27i + 22j + 83k

Q: Find the length of the vectors (a) 2i⃗ +3j⃗ −k⃗

A:

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

A:

Q: Find the magnitude and direction (in degrees) of the vector. v = 4i + 4V3j

A:

Q: Consider the vectors. 6i- j, -8i + 4j (a) Find the dot product of the two vectors. -52 (b) Find the…

A:

Q: Find a vector that has the opposite direction of a = 8i - 6j and twice the magnitude.

A: a=8i-6j

Q: In the previous question, what is the angle between the two given vectors to the nearest degree? a)…

A:

Q: Find the unit vector in the same direction as v = 8i - 15j.

A: The vector given to us is  v = 8i - 15j

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: Given vectors a= (2, 1) and b= (−3, 5), find −2a+4b. Write your answer in component form

A: To find the component form of a vector

Q: Find the angle between the vectors ū = 5i – 5j +k and v = 2i + 16k.

A:

Q: for what value of Ca) will the Vector ū = -41-8)4ak,ū =ei+4j-5k are parallel

A:

Q: Give two vectors A=4i+3j, B=5i-2j Find its values and the direction of vector C, which is 2A-B

A: Vector addition

Q: Given the two vectors A = -9j- 2 -7k and B = -31- 4j +8k, Find the (a) A + B (b) A B (c) -4A…

A:

Q: Find the angle between two vectors, 6 and 8 units long, when their resultant is (a) 10 units long…

A: Given: The angle between two vectors, 6 and 8 units long

Q: : For given vectors, a-2i - j+ 2k and b=-i + j- k, find the unit vector in the direction the vector…

A:

Q: Given vectors a = (-3, 6) and b = (5, 1), find 2a +3b. Write your answer in component form. 2a + 3b

A:

Q: Find the components and length of the following vectors:(a) 4i + 3j

A: Given4i+3jTo find component and length

Q: given the vectors u=-i-5j and w=-3i+2j, find -4u and u-w. write your answers in the form ai+bj

A: Let u→=u1i∧+u2 j∧+u3 k∧ and v→ = v1 i∧+v2 j∧+ v3 k∧be two vectors , then the sum of  u→  and v→  is…

Q: Given the vectors u = -i-4j and w=-2i+5j, find 7u and u – w. | Write your answers in the form ai+bj.…

A: Given the vector u = -i - 4j And w = -2i + 5j Find 7u and u - w in the form of ai + bj.

Q: Obthe resulting parallelogram from the following two vectors that form non-parallel sides A = 3 + 2…

A:

Q: What is the area of the parallelogram formed using the vectors below as 2 sides of the…

A: First we will find out the vectors from the graphs ,

Q: Find the angle in degree between the two vectors as indicated in the rectangular box of dimension…

A: *to find:- angle between the vectors u & v.

Q: = 3. 6. Find the magnitude of the resultant of two vectors u and v, given = 5 and the angle between…

A: Explanation of the answer is as follows

Q: Find the components and length of the following vectors:(a) 2i − 3j

A: 2i - 3j

Q: use the vectors v=-2i+j and w=4i+3j to find: Find a unit vector in the same direction as v.

A: A vector is a quantity that has both direction and magnitude and a unit vector is a vector that has…

Q: Find the magnitude and direction angle of the resultant of each pair of vectors. t = (17, 12) u =…

A: We use vector additions.

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: 3. Find the magnitude, ||||, of each of the following vectors: a. = -51 + 12j b. = -i- j

A:

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

A:

Q: Find a unit vector in the same direction as the given vector. a = 40i + 9j

A: Given,           The vector is a=40i+9j .

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

A: The vectors 4i^-j^, -3i^+2j^

Q: For the pair of vectors, find 4U +3V. %3D

A: In a product of one vector with a scalar quantity, the scalar quantity is to be multiplied with all…

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

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

A: Given: 6j, -4i

Q: Find the angle between the given vectors to the nearest tenth of a degree. U = 13i - 4j, V = 2i +…

A: For two vectors a and b we know that their do product is a·b=abcosθthen cosθ=a·bab…

Q: Find the angles between these vectors, giving your answer in degrees to one decimal place. ) -3 and…

A:

Q: What is the area of the parallelogram formed using the vectors below as 2 sides of the…

A: What is the area of the parallelogram formed using the vectors t̄ and s̄ as 2 sides of the…

Q: Given the vectors i = 10i – 5j and i = 9i + j, perform the operations below. 8- i- 5- = Calculator…

A:

Q: Find the angle in degree between the two vectors as indicated in the rectangular box of dimension…

A: The dimension of the given box is 1×2×3.

Q: Given vectors a = (2, 6) and b = (1, -3), find - 3a+5b. Write your answer in component form. -3a +…

A: We need to find the sum of given vectors.

Q: Given the vectors v=7i-5j and w=−i+3j, find −9v and v-w. Write your answers in the form ai+bj.

A:

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: Given the vectors M = -10ax+4a, – 8a, and N= 8ax+ 7a, – 2a-, find: (a) a unit vector in the…

A:

Q: Find the angle between the vectors i – k and 4i + 4j -2k

A:

Q: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

Q: Find the magnitude and direction of the resultant of the following vectors using Laws of Sines and…

A: Given that x=10N and Y=5N. The graph formed is, Now decompose X and Y vector along x and y…

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

A: (a) part Consider the given vectors 9i   ,   5i+4j Suppose the given vectors be  u→  and  v→ such…

Q: b) For what values of A, the vectors 2i -j+ 2k and 3i + 22 j are perpendicular?

A: If we have two vectors ai^+bj^+ck^  and a'i^+b'j^+c'k^ , then, these vectors are said to be…