10. Given points. P(2,5,-1). Q(-1,-4,1), and 7(5,0,2), find: (a) the vector Reg: (b) a unit vector in the direction of Regi (c) the length of the perimeter of the triangle PQT; (d) the interior angle at Q: (e) the vector projection of Reo on Rer: (f) the length of the altitude of the triangle that extends from Q perpendicularly to the opposite side or its extension.

Q: The unit vector which is perpendicular to both r1=8ax+3ay- 2az , r2=2ax+7ay-6az is equal to

A: Given, vectors arer1=8ax+3ay-2az, r2=2ax+7ay-6azThe unit vector perpendicular to both vectorsr1, r2…

Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: Q2: Find the vector and unit vector (u) in the direction of the vector P2 = (-3,0, 6) to P, = (4, 6,…

A: Let us consider the vector P=(a,b,c) and Q=x,y,z. The vector in the direction of P to Q is obtained…

Q: Given vector u= (-3, 3) and v = (6, –2), determine the value of 4u + v in | component form.

A:

Q: 21. Given F₁ = 3î - 2ĵ+ 4k and F₂ = 5j + k, find: a. Dot product, F₁ F₂ = b. Dot product, F₂ · F₁ =…

A: As per our guidelines we are suppose to solve only first three subparts if the multiple parts are…

Q: For the given vectors: å = (-2,-3), 5 = (1,–2), 7 = (0,3), find: (a) 2å – 35 + ở (b) angle between…

A: Given the vectors a,b and c. The solution to the given questions are as follows.

Q: Let u = (6, 2, 4) and v = (1, 2,0). Find: (a) d(u, v). (b) the angle 0, in radians, between the two…

A: See the detailed solution below.

Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: 2. For v = (5,-2) and w = (3, 4), find v+w, v - w, v/2, -w and make one sketch labeling all 6 of…

A: Given,           v=<5,-2> and w=<3,4>

Q: Find the projection of vector A=(6,7) along vector B=(1,4).

A:

Q: Find the direction angle of the vector u=

A:

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

A:

Q: 3. Consider the following vectors: (2,3) & (-5,1) a. Find the dot product between them b. Find the…

A: We have to find the dot product and angle between two vectors.

Q: The vector v is 10 units long and makes an angle of 30° with the positive x-axis. What is the…

A:

Q: 5. For vectors given the vectors v =(-4,-3) and w (-1,-1), find: (a) Sketch, v+w below. Find its…

A: We can solve as follows

Q: For the given vectors: å = (0,3), b = (4, –2), ở = (3,2), find: (a) 3å – 6+ 2č (b) angle between the…

A:

Q: 2. Given the points X(-3, -1, 5) and Y (4, 4, -9): A. Write the position vector OX in vector form:…

A:

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: 22. Given vectors C = 5î - 2ĵ and D = 3î + 4ĵ, find: a. the projection of vector Conto the x-axis…

A:

Q: Q5) Given points A (10, -3, 4) and B(-4, 3, 5), find: a. The distance from A to B. b. A unit vector…

A:

Q: Given point Al-4, -5, 8) and point B(3, 0, 6). let be the position vector from the origin to point A…

A: Given;           Origin:0,0,0Point A: -4,-5,8Point B:3,0,6 Position vector…

Q: For the given vectors: å = (-3, –3), B = (1,–2), ở = (1,3), find: (a) 2å – 35 +ở (b) angle between…

A:

Q: Given the points A: (-2,2,-6) and B: (4,3,6), find the vector u = AB u = <

A: