3.) the a. Find the distance between point and the line given by the set of parametric equations. ( Round answer to three decimals) (1,-7,2); x = 2t, y=t -3, z =2t +2 b. Verify that the two lines are parallel, and find the distance between the lines ( Round answer to three decimal places) Li:X=2-4, y=3+3t , z =4+2t La: X=5t, y=| - 15t, Z =4-107

Q: iv) y=-x- 3 1 v) y=-2x+ vi) y=;* 1 21 y y y 1 =-2.5 1 2 2 y y y 2 2 2 -2 -2 -2 2 -2 2 2 y-intercept:…

A: We have to write equation in the form x/a+y/b=1 for y-intercept , here b is y-intercept

Q: A straight line passes through points A(-1,4) and B(0, -3). Write the equation of the line under:…

A:

Q: 21 6) x-1. y

A: Given query is to write the equation in the form of rectangular form.

Q: For the lines: L1: x=2-4t, y= 5t, z=1+2t L2: x=-7-k, y=2+3k, z= 5+k Find the parametric equations of…

A: The line passing through the point (a,b,c) and parallel to z axis is  (a,b,c)+t(0,0,1)  That is ,…

Q: . Let A=(2, 3, 1) and B= (4, -1, 2) and C = (6, 2, 3). Find the equation of the line in parametric…

A:

Q: 3. Write parametric equations for each geometric object. (a) line passing through the points (-3,4)…

A: Give, Line passing through the points -3, 4  and 2, -7 Circle with center -6, -1  and radius 2.5…

Q: . Let A=(2, 3, 1) and B=(4, -1, 2) and C = (6, 2, 3). Find the equation of the line in parametric…

A:

Q: Find the obtuse angle formed by the lines x+3y+3=0 and x-y-2=0.

A: Topic - angle between lines We will take absolute value of angle as sign depends Up on which line we…

Q: 6. Write the equation in slope intercept form of the perpendicular bisector of a segment with…

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-2,-2)…

A: Solution is given below:

Q: The point Q(-7,7) is translated by T[23] and then receded with the y=-x axis then the resulting…

A:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-5, 0,…

A:

Q: Which values for x and y make lines r, s, and t parallel? Express your answers as decimals rounded…

A:

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.