A plane is traveling at a speed of 650 mph at a bearing of 60°  West of North.  It is flying in wind with a speed of 70mph at a bearing of 40° South of West.  The resultant vector represents the actual velocity of the plane. Write the resultant vector in component form.

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

A: a=8i-6j

Q: An airplane is on a heading of 235° at 600 km/h and a l10 km/h wind is blowing from due west.…

A:

Q: Explain how you would convert the vector a = 5 km with a bearing of 135° in Cartesian form.

A: Given a→=5 km and bearing of vector θ=135°

Q: The vectors a(3;-4) and b(x; 9) are perpendicular to each other. Calculate the magnitude of the…

A: Given vectors are: a→=3,4 and b→=x,9

Q: Find a unit vector in the direction of v. v = 12i - 35j

A:

Q: Find a vector of magnitude 7 in the direction of v = 12i - 5k

A: Given vector is v = 12i – 5k. First find the direction of the given vector

Q: Sketch the vector v = -6i - 2j as a position vector and find its magnitude.

A:

Q: Determine the length of the crankshaft AB by first formulating a Cartesian position vector from A to…

A: Let us first write the Cartesian position vector from A to B like…

Q: Sketch the vector v = -4i as a position vector and find its magnitude.

A: Plot the vector –4i as shown below.

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:

Q: Sketch vector v = -i - j as a position vector and find its magnitude.

A: Given vector is  v=-i-j

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

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

Q: A small plane is flying north in calm air at 250 mph when it encounters a horizontal crosswind…

A: Given data The plane is flying north in calm air at 250 mph. Speed of the horizontal crosswind…

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: Sketch vector v = 5i - 2j as a position vector and find its magnitude.

A: Given vector is v=5i-2j. Draw the position vector.

Q: The vector from the origin to point A is given as 6a, – 2a, - 4a., and the unit vector directed from…

A: Vector A is <6,-2,-4> Let Vector B i s <23B,-23B,13B> The distance between A  and B  are…

Q: Sketch the vector v = -3i - 4j as a position vector and find its magnitude.

A: Given: v = -3i - 4j

Q: Find the angle between vectors and

A: Given vectors are same i.e. they are parallel.

Q: Find a unit vector in the direction of the given vector

A: Given:        v=-9,-12 Unit vector formula is the vector divided by its magnitude.  The formula for…

Q: What is the component form of a vector with a magnitude of 17 and a direction of 125°?

A: To find the component form of the vector whose magnitude and direction are given.

Q: Find a vector of magnitude 3 in the direction opposite to the direction of v = i+j - k.

A: here we use the formula , v→=-v→v→

Q: Find the components of the vector with magnitude 5 and direction θ = 2π/3

A:

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

A:

Q: A motorboat sets out at 10 am from a position (-6i – 2j) km relative to a marker buoy, and travels…

A: please see the next step for solution

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: A pilot is heading his plane N 76°W at an airspeed of 950km/h, while wind is blowing in the…

A: Given: A pilot is heading his plane N 76 degree W at an airspeed of 950 km/hr, while wind is blowing…

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

A:

Q: A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is…

A: Solution....

Q: Find the magnitude of the horizontal and vertical components of the vector with magnitude 2 pounds…

A: Vector components as per trigonometry.

Q: Find a vector of magnitude 3 in the direction opposite to the direction of v = ± i + ±j - k.

A: Let u be the vector to be found. To find u, first we need to find the direction of the vector v. To…

Q: Calculate the angle between the vectors and . Write your final answer in radians, either as an…

A:

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

A: Given vector is

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: Given P-4,1, Q3,-4, R2,6 To find the unit vector with the same direction as QR→

Q: A leaf is floating on a river to the S30°E at 6 km/h. A wind blows to the west at a rate of 3 km/h.…

A: Given : Leaf is floating at 6 km/h and wind is blowing at 3 km/h

Q: Find the magnitude of the horizontal and vertical components of the vector with magnitude 2 pounds…

A:

Q: Find the component form of the indicated vector.

A: The given question belonging to the vector in which we have to find the value of subtraction of the…

Q: A plane is flying with an airspeed of 140 miles per hour and heading of 155∘degrees. The wind…

A: Let P be the speed of the plane. Let W be the direction of the wind. Let T be the ground speed and…

Q: Find the unit vector in the same direction as

A:

Q: A sailboat is sailing at a speed of 6 knots at a true bearing of 220°. Give the velocity of the…

A: First represent the vector on coordinate plan than break the components along x & y-axis.

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: Find the ordered pair that describes the vector whose magnitude is 10 and whose angle of rotation is…

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: Sketch the vector v = 2i + 3j as a position vector and find its magnitude.

A: Given vector is v = 2i +3j. Draw the vector as shown below.

Q: Write the vector v in terms of i and j whose magnitude||v|| and direction angle θ are given.

A: Any vector can be break down into its components if we know its magnitude and its direction. The…

Q: A rifle at A is fired at a target at B. If the speed of the bullet is 1800 ft/s, determine the…

A: Let θ be the angle with the x-axis Then the rectangular form will be  v=1800cosθi+1800sinθj  ft/s

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

A:

Q: Use the dot product to find the angle between the position vectors A and B.

A: Given: