4. Given that A(1, 1, – 3), B(5, 4, – 1) and C(2, – 1, – 5) are three points in the 3-dimensional coordinate system with O as the origin. (a) D is a point on the line segment AB such that AD : DB = 3 : 4, find the coordinates of D. (b) Find AB and AC. (c) Find AB · AC.

Q: For what values of z and y is orthogonal to both (-1 and

A: Remark: We know that two vectors are orthogonal if they are perpendicular to each other. i.e., the…

Q: Question 16. Let i =i– 23+2k and ỹ= 37+43– 2k be the position vectors of X and Y. The points X, Y…

A: The solution is given as follows

Q: 21° 57⁰ E +y 38° C C = 82 m/s D = 62 m/s E = 41 m/s Figure 3-31 Question 3-34. +x

A: Vectors are quantities with both magnitude and direction. Here we are given three velocity vectors…

Q: Classify the following diferential equations. Write the order, linearity and the homogeneity of the…

A: Sol:- (a) y'''+ex y'' = x3+5xy2 order :- 3 :- as Highest order of differential equation is 3…

Q: 20b. Find the coordinates of A' after A(-3, 4) has been reflected: Reflection in the x-axis: A'= I…

A: To find the reflections

Q: Prove that for A # B, AB S AB S AB.

A:

Q: Let u = PQ and v = PR ; where P = (2, – 1, 3) Q = (0,5, 1) and R = (5,5,0) find a. The component…

A:

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: b. Solve the following equations using Cramer's Rule 4x + 2y = 10 Зх— 5у %3D 1

A:

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

A:

Q: Given the points C(-4, –5) and D(-1, 1), express the vector CD in terms of i and j.

A:

Q: 15. Find the Cartesian equation of the following lines: a. parallel to the line r= 2i+3j+4k +1(3i –…

A:

Q: 3. Find the angles a, ß,y, which the vector Á = 3î – 6î + 2k makes with the coordinates axes and…

A:

Q: 6. The picture is aligned with the coordinate axes such that point D is at the origin (0,0) and…

A:

Q: Given vector u = (-3,2) and v = (-3, –1) , determine the value of v – 2u ir component form.

A: We can determine the component form as below.

Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

A:

Q: Given the points A(3,5) and B( – 3, – 7), find d. the scalar equation of the line.

A:

Q: Rotate points P/(1,1,1), P2(2,1,2), P3(2,3,1) & P4(1,3,2) +30° around

A: Here, in the question We have to rotate the points about the points P1(1, 1, 1) , P2( 2, 1, 2),…

Q: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

A:

Q: Consider the following diagram. The point O represents the origin of the zy-plane. The shape BCDE…

A:

Q: b. The complex numbers z, and z2 are given by z = V3 + V3i and zz = V3-i Plot the points…

A: