straight river flows east at a speed of 12 mi/h. A boater starts at the south shore of the river and heads in a direction 60° from the shore (see the figure). The motorboat has a speed of 24 mi/h relative to the water. (Assume that the i vector points east, and the j vector points north.)   a) Express the velocity of the river as a vector in component form. b) Express the velocity of the motorboat relative to the water as a vector in component form. (Round your answer to two decimal places.) c) Find the true velocity of the motorboat. (Round your answer to two

Q: Express the vector in terms of the unit vectors i and j. 2(3, 3) + 3(4, 2)

A:

Q: Find the unit vector in the direction of v and verify that it has length 1.

A: If vector u is given, then the unit vector in direction of vector u is given as,

Q: 3. A pilot flies with a ground velocity of 280 km/h on a bearing of 292°. There is a 55 km/h wind…

A:

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: Find the magnitude of the vector

A: The given vector is 0,7We know that in a vector a,b the magnitude is a2+b2

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

A:

Q: Find a vector v whose magnitude is 4 and whose componentin the i direction is twice the component in…

A: Given: magnitude of the vector  is 4  The component of the vector  in the i direction is twice the…

Q: Find the parallel projection of the vector v = onto the vector w=.

A: Given problem:- Find the parallel projection of the vector v=<4, -5, 7> onto the vector…

Q: What is the difference between a vector and a scalar?

A:

Q: A unit vector in the direction of the given vector is

A:

Q: Find the vertical component of a vector, where the inclination  Θ of the vector from the horizontal…

A:

Q: find the given vector  Vector of length 2 in the direction opposite to v = i − j

A: A vector oppositely directed to v=i-j is is u=-v=-i-j=-i+j                   u=-i+j A unit vector eu…

Q: If a 350-lb load is suspended by two chains as shown in the figure to the right. What is the…

A:

Q: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of 67o67o…

A: Given: A bullet is fired into the air with an initial velocity of 950 feet per second at an angle of…

Q: A forklift is used to offload freight from a delivery truck. Together, the forklift and its contents…

A:

Q: Find a vector v whose magnitude is 6 and whose component in the i direction is four times the…

A:

Q: A boat is motoring directly north at 5 miles per hour. At the same time, an 8 m.p.h. wind is blowing…

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

Q: Find the magnitude of the vector.

A: The given question is taken from the vector in which we have to find the magnitude of the given…

Q: Find a vector v whose magnitude is 3 and whose component in the i direction is five times the…

A:

Q: A person swims 6.4 meters per second north while being pushed by a current moving west at 2.1 meters…

A:

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: A small plane is flying horizontally due east in calm air at 150 mi/hr when it is hit by a…

A: Let's find.

Q: A pilot heads his jet due east. The jet has a speed of 450 mi/h relative to the air. The wind is…

A: Let's solve all given questions.

Q: Calculate the magnitude and direction of the resultant of the two acceleration vectors shown

A:

Q: Find a unit vector u with the same direction as vector v =

A:

Q: Find the magnitude of the horizontal and vertical vector componentsfor a vector.

A: By taking the the vector to be analyzed as the hypotenuse, the horizontal and vertical component can…

Q: Find the unit vector in the directions of v, where Ans = %3D

A: To find unit vector in the direction of v, divide it by the length of v.

Q: Find a vector v whose magnitude is 3 and whose componentin the i direction is equal to the component…

A: Given- a vector v whose magnitude is 3 and whose component in the i direction is equal to the…

Q: and the unit vector along the direction of u.

A:

Q: Find the unit vector in the direction of

A: Unit vector in the direction <-2, -5> Unit vector have magnitude 1

Q: Find the unit vector in the same direction as vv=5i-j

A: Given vector is

Q: Explain how to find the unit vector in the direction of any given vector v.

A: To find the unit vector in the direction of the given vector v, divide the vector v by its…

Q: A bird is flying south at a rate of 45 miles per hour while being pushed east by wind with a speed…

A: Given- Bird's flying rate in the south=45miles/hrBird pushed by wind in the east=12 miles/hrWe need…

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

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} =…

Q: A pedestrian walks at a rate of 6 km per hour east. The wind pushes him northwest at a rate of 13 km…

A: We can find the answer as below

Q: Find the magnitude of the vector u =

A:

Q: Find the unit vector in the same direction as

A:

Q: Find a unit vector, u, in the same direction as vector v = .

A: Recall: Unit vector:  Let u→ be any vector then unit vector is            u∧ = u→u→

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

A: We have the vector is (0, 1)   We have to find the vector obtained by rotating (0, 1) through an…

Q: A truck is traveling due north at 55 km/hr approaching a crossroad. On a perpendicular road a police…

A:

Q: Vector ä has a magnitude of zo and poin ts 60' Norte of East. Caleulate the * and comporents of À

A:

Q: find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

A: Find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: A small plane is flying horizontally due east in calm air at 175 mi/hr when it is hit by a…

A: Plane is flying horizontally du east calm air at 175 mi/ hr. Hence, Vplane=175i Now, horizontal…

Q: Assuming vector B is 12 units long, vector 4B is:

A:

Q: A vector has an x-component of −26.0 units and a y-component of 45.0 units. Find the magnitude and…

A: Explanation of the solution is given below..

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…

Q: Express the vector v = 4i + 2j - k in terms of magnitude and %3D direction.

A:

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.