The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find their angle of intersection, 0, correct to the nearest degree.

Q: Write the equations of the lines tangent to the curve y x- 4x at both a 0 and a 2. Then, determine…

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Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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Q: The equation of motion of a body performing damped force vibration, Is given by t 5dx +6x = Cos t,…

A: Given DE is d2xdt2+5 dxdt+6x=cost also given conditions are x(0)=0.1 and x'0=0 solve the equation

Q: Evaluate the slope at the point (2, 0) for: y² + sin(y) = 3x² - 12

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Q: Find an equation for the line that is tangent to the curve y = 5x - 5x at the point (1,0). The…

A: Our Aim is to find an equation for the line that is tangent to the curve y=5x3-5xat the point (1,0).…

Q: Find the acute angle between 3x – 2y + 7 = 0 and 2y + 4x – 3 = 0 (to nearest degree).

A: Given, 3x-2y+7=0      .....12y+4x-3=0      .....2

Q: Find the angles at which the curve y=x3−x intersects the x-axis.

A: The angle at which curve intersect the x axis is determined by the angle of slope of tangent to the…

Q: Find the angle between y=5x2-3 and 3xy-9x2-x

A: Given y=5x2-3 --- Eq 1 and 3xy=9x2-x      --- Eq 2We know that angle between y1=k1x+b1 and y2=k2x+b2…

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.