Analytic Geometry Answers

Pls Help *MTH282*

Suppose the position vector of X and Y are (1,2,4) and (2,3,5), find the position vector of a point Z that bisect XY in the ratio 2:3

A 7i+12j+22k

B. 7i-12j+22k

C.frac{1}{7} (7i+12j+22k)

D.frac{1}{17} (7i-12j+22k)

v1(3,-2,-2), v2(2,-1,-2), v3(-1,1,1) , u(0,1,h)

find all values of h such that u is a linear combination of v1, v2 and v3

Suppose the position vector of X and Y are (1,2,4) and (2,3,5), find the position vector of a point Z that bisect XY in the ratio 2:3.


a.\\(7i+12j+22k\\)

b.\\(7i-12j+22k\\)

c.\\(\\frac{1}{7} (7i+12j+22k)\\)

d.\\(\\frac{1}{17} (7i-12j+22k)\\)

The quantity αdot (\eta times gamma)is called the ____


a.scalar-vector triple product

b.scalar-vector product

c.vector triple product

d.scalar triple product

Determine the value of a, so that If α=2i+aj+k and \eta=4i−j−2k are perpendicular.


a.2

b.5

c.4

d.3

Vectors with same direction (parallel), opposite sense but different magnitude are called



a.unlike vectors

b.like vectors

c.unit vectors

d.equal vectors

If α=α1i+α2j+α3keta=\ eta1i+\ eta2j+\ eta3k, thenαdot \etaαdot\ eta is ____?


a.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}+\\alpha_{3}\\beta_{3}\\)

b.\\(\\alpha_{1}\\beta_{1-\\alpha}\\beta_{2-\\alpha}\\beta_{3-\\alpha}\\)

c.\\(\\alpha_{1}\\beta_{1}-\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)

d.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)

If α=α1i+α2j+α3keta=\ eta1i+\ eta2j+\ eta3k, thenαdot \etaαdot\ eta is ____?


a.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}+\\alpha_{3}\\beta_{3}\\)

b.\\(\\alpha_{1}\\beta_{1-\\alpha}\\beta_{2-\\alpha}\\beta_{3-\\alpha}\\)

c.\\(\\alpha_{1}\\beta_{1}-\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)

d.\\(\\alpha_{1}\\beta_{1}+\\alpha_{2}\\beta_{2}-\\alpha_{3}\\beta_{3}\\)