Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the vector v is the negative reciprocal of the slope of the given line. ..... Determine the slope of the vector v = ai + bj.

Q: Show that v = ai + bj is perpendicular to the line ax+ by = c by establishing that the slope of the…

A:

Q: Show that direction vectors of the lines Le and are orthogonal.

A: Given lines are  L1=x-32=y+14=z-2-1L2=x-35=y+1-2=z-32 To prove the directional vectors of these two…

Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope…

Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

A:

Q: Show that the lines L1 : x = 4 – t, y= 2t, z = 5+t and L2 : x = 1+4t, y= 3 – 8t, z= 5 – 4t are…

A: Let's find.

Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

A:

Q: True or false? If v is a direction vector for a line L, then −v is alsoa direction vector for L.

A: True or false. If v is a direction vector for a line L, then -v is also a direction vector for L.

Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

A:

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 5+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

A:

Q: Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

A:

Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

A:

Q: | Find a vector equation for the line through the point (–9, –9, 3) parallel to the line 19 + 4t, y…

A:

Q: Part 1 of 4 Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

A:

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: Show that the lines L1 : x = 2 – t, y = 2t, z = 1 +t and L2 : x = 1 + 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=2-t, y=2t, z=1+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. X - 8 y + 2 = z +…

A: This question is based on 3-d coordinate geometry.

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

A:

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = :5+t and L2 : x = 1 + 4t, y = 3 – 8t, z = 5 – 4t are…

A:

Q: The vectors and are parallel. True False

A: Recall: ⇒ Two vectors are parallel if one is a scalar multiple of the other.         i.e, Let a→ and…

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: In the given diagram, which is the equivalent of vector

A: sum of vectors of closed triangle is 0 if we choose one direction -- Here if choose anticlockwise…

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 1+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A:

Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

A:

Q: Show that the lines L1 : x =1- t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

A:

Q: through the point (−2,4) and is perpendicular to the line  x=[31]+t[4−5] is

A:

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c

A: Find the slope of the given vector v=ai+ bj is given by ba.

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

A:

Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

A:

Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

A:

Q: Show that the lines L1 : x = 2 – t, y = 2t, z =1+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

A:

Q: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5 +t and L2: x = 1+4t, y = 3 – 8t, z = 5 – 4t are…

A:

Q: Show that the lines L1 : x = 3 – t, y = 2t, z = 3+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

A:

Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

Q: Show that the lines L1 : x =1 – t, y = 2t, z = 5+t and L2 : x 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A: Let's find.

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: a) The line y =- 5x + 9, in VECTOR form (R?).

A:

Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

A:

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…