A particle P moving a constant velocity i+j+ k passes through a point with position vector 3i – 7j - 4k at the same înstant as a particle Q passes through a point with position vector -i+j+\k. Q has a constant velocity vector 2i – j- 5k (a) Find the velocity of Q relative to P. (b) Find the value of A if P and Q collide. (c) If A = -1/2, find the shortest distance between P and Q.

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: 4

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Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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Q: A particle moves at constant speed 1445 units along the curve of intersection of the two the two…

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Q: Find a vector equation for the line through the point P = (-3, 5, -4) and parallel to the vector v =…

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Q: The position of a moving particle in space is vgiven by r(t) = (- 76- 21) i + (108t° - 2890) j +…

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Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…

Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

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.