7.(a) A and Care the points (1,3, –2) and (4,–4,4) respectively. Point B divides AC in the ratio 1:2. Find the coordinates of B. (b) kAČ is a vector of magnitude 1, where k > 0. Determine the value of k.

Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

A:

Q: What is the direction of the vector with an initial point of (3,-5) and a terminal point of (8, 6)?…

A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: Find the vector v with the magnitude.15/2 and direction of u = For the toolbar, press ALT+F10 (PC)…

A:

Q: Let ā = (1, – 5, 2) and b = ( – 1, 5, 3). %3D Find the angle between the vectors (in degrees).

A: We know that for two vectors a→ and b→,   cos(θ)=a⇀.b⇀|a||b|⇀⇀ where θ is the angle between vectors.…

Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

A: Given- A=(1,2,0) , B=(3,4,-1), C=(4,5,2) To find the exact value of distance between point C and the…

Q: 40. Given a = (3,-4) and b = (1, 2). Find the vector a + 2b a. (5,-8) b.(5,0) c.(4,-4) d. (4,0)

A: Given,

Q: Q4. Determine whether the vectors are linearly dependent or independent. v1=(4,-2, 2), v2 = (5, 4,…

A: v1=4-22, v2=54-3, v3=-793 We have to check whether the given vectors are linearly dependent or…

Q: Find the direction angle to the nearest degree for the vector v = =

A: Step 1:​v=⟨−3,6⟩​Step 2:​Direction angle of ⟨a,b⟩:θ=tan−1(xy​)We…