Given the vector r(t) = { cosineT, sineT, Ln (CosineT) } and point (1, 0, 0) find vectors T, N and B at that point. Vector T is the unit tangent vector, so the derivative r(t) is needed. Vector N is the normal unit vector, and the equation for it uses the derivative of T(t). The B vector is the binormal vector, which is a crossproduct of T and N.

Q: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R…

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

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

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Q: A missile is fired from ground level with an initial velocity of (0) - (1000, 1400, 368) measured in…

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Q: Find the angle a in radians between the vectors απ -3] and

A: Step 1: Given vectors: u=[−3−1​] and v=[1−2​] Step 2: To find the angle 𝛼 between two vectors a and…

Q: Sketch your process of determining the vector and find its component form if 7 makes the angle of…

A: Here we can use easy method like spherical coordinates to solve this question. Here magnitude and…

Q: Find the values of x such that the angle between the vectors and is 45°.

A: Given that The angle between the vectors 6,1,-1 and 1,x,0 is 45°.

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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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.