Express the vector in terms of it's length and direction. Velocity vector v = (-2 sin t)i + (2 cost)j when t = pi/2.

Q: Find the horizontal and vertical components of the vector v that has magnitude |v|=2 and direction…

A: Given, magntude of the vector =v =  2 and direction  β (angle with the +x axis)=45o  We have to find…

Q: Find the velocity and acceleration vectors in terms of u, and u. r= a(9 + sin t) and 0 = 3 - e ',…

A: we derivative to find velocity and acceleration

Q: s opposite direction to the vector u = .

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Q: Find the angle 0 between the vectors. (f. 9) = L R f(x) = 3x³, g(x) = 4x4, %3D f(x)g(x) dx radians

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Q: The wind is blowing at 20 miles per hour in the direction N30°W. Express its velocity as a vector v…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: forces acting at a point P are given as 30 pounds with N10°E and 80 pounds with N 80° E. Approximate…

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Q: The motion of a particle is defined by the position vector r = A(cost + t sint)i + A(sint – t…

A: Given position vector is, r→=Acost + t sinti^ +Asint - t costj^ Then the acceleration vector is the…

Q: The jet stream is blowing at 60 miles per hour in the direction N45°E. Express its velocity as a…

A: The jet stream is blowing at 60 miles per hour in the direction N45°E We need to express its…

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sin 2t and 0 = 4t v=u, +Due…

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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 velocity and acceleration vectors in terms of u, and ug- r= a(4+ sin t) and 0 =9- e -t,…

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Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: How do you find a vector's magnitude and direction?

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

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Q: Find the acceleration vector for the position vector 7 (t) = (sin(11t), 3t', e -*). x component = y…

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Q: Find the component form of the unit vector that makes an angle 0 = 3 2л with the positive x-axis.

A: We have to write the component form of the unit vector which makes an angle -2π/3 with positive x…

Q: Find the velocity vector for the position vector r(t) = (sin(12t), 8t°, e-6*). x component = y…

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: Determine the angle that the vector [-1, -1] makes with the positive horizontal X-axis

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Q: Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

A: Given that, y=x3   We have to find a unit vector parallel to the tangent line of the given curve at…

Q: Find the velocity and acceleration vectors in terms of u, and ug- = 5 sin t and 0= 5t = ( 5 cost)u,…

A: Topic:- application of derivatives

Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

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Q: A baseball is thrown with a speed of 70 mph at an angle 14 degrees of from the horizontal. Write the…

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Q: Find the horizontal component of the vector if |V|= 4 and theta =50°

A: given |V|= 4 θ=50° horizontal component =|V|×Cosθ

Q: Subtracting the two equations, find a vector equation for the curve of 3 intersection between y =…

A: Here, the two equations are y=4x2+34z2  and  y-1=3x2+12z2 for x>0. We will be finding a vector…

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 direction of

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

Q: Find the angle 0 between the vectors. (G E i+ sin (-)j u=COS V=COS i+ sin

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Q: Find the angle 0 (in radians) between the vectors. U = COS i + sin (學) 2T V = COS sin()3 + sin j 0…

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Q: If the wind is blowing at 12 mi/hr in the direction N40°W, express its velocity as a vector v.

A: Given the wind is blowing at v=12 mi/hr in the direction of N40°W as shown below:

Q: Find the angle e between the vectors. -(cos , sin 2), v- (cos , sin. x radians

A: Given that, u=cos3π4,sin3π4 and v=cosπ6,sinπ6. It is known that, the formula for u·v=u·v·cosθ.…

Q: Find the cross product of the unit vectors j × k and sketch your result.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: If v = 3i - 4j is a velocity vector, express v as a product of its magnitude (its speed) times its…

A: To Determine: If v=3i-4j is a velocity vector, express v as a product of its magnitude (its speed)…

Q: Find the unit vector in the direction opposite (-2, –1). to y =

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Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(3t))…

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Q: Find the unit vector in the same direction as

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Q: A force of 6 newtons is applied in the direction of the vector v = 2i + 2j - k. Express the force F…

A: Given vector, v=2i+2j-k

Q: Find a unit vector in the direction of the vector v = .

A: Given a vector v=<-2,2>. We need to find a unit vector in the direction of 'v'. Let's begin.

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: and ue. Find the velocity and acceleration vectors in terms of u, r= 5 sint and 0 = 8t

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Q: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sint and 0= 9t Ou, + (O ue V…

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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Q: Find the unit vector in the same direction as v = 5i - 12j. Then verify that thevector has magnitude…

A: Unit vector in same direction vectorvector's magnitude

Q: (b) Find the direction e of the vector u = .(angle between the positive x-axis and the vector)

A: Topic = vector

Q: Find the velocity vector for the position vector r(t) = (sin(3t), 10t°, e -"). x component = y…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.