1. ## hard vector questionsss

could someone help me with the followibg vecrot questions please:

1) Let A, B, C and D be the points with coordinates (1,3,4),(2,0,7),(3,5,−1) and (5,−1,5) respetively.

a) Write down the vector AB in the form ai + bj + ck.
b) Find the coordinates of the point E which is on the line AB between A and B and twice as far from A as from B.
c) Find the coordinates of another point on the line AB which is twice as far from A as from B.
d) Find the coordinates of the point H which divides the line BD in the ratio 2:3.

2) .For each of the following planes, give a vector equation of the form,
x = a(s,t)i y= b(s,t)j z=c(s,t)k,
where a(s,t),b(s,t),c(s,t) are expressions involving the parameters s and t, and hence parametric equations of the form,
x = a(s,t),y = b(s,t) and z = c(s,t), where x = xi+yj+zk.

a)The plane through the points with coordinates (3, −1, 5) and (2, 8, −6) and parallel to the vector
8i−j+6k;

b)The plane containing the triangle ABC, where A, B and C have position vectors a = 3i − 4j + 2k,
b = 8i+9j−4k and c = 4i−3k;

3) Does the line through the point with coordinates (3, −5, 1) in the direction of the vector i + j − k meet the plane through the points with coordinates (3,−1,5) and (2,8,−6) and parallel to the vector 8i − j + 6k? If so, find the point(s) of intersection.

4 A rhombus is a parallelogram, all of whose sides have the same length,Show that the diagonals are perpendicular.

thank you !!!

2. Originally Posted by riotsandravess
could someone help me with the followibg vecrot questions please:
1) Let A, B, C and D be the points with coordinates (1,3,4),(2,0,7),(3,5,−1) and (5,−1,5) respetively.
a) Write down the vector AB in the form ai + bj + ck.
b) Find the coordinates of the point E which is on the line AB between A and B and twice as far from A as from B.
c) Find the coordinates of another point on the line AB which is twice as far from A as from B.
d) Find the coordinates of the point H which divides the line BD in the ratio 2:3.

2) .For each of the following planes, give a vector equation of the form,
x = a(s,t)i y= b(s,t)j z=c(s,t)k,
where a(s,t),b(s,t),c(s,t) are expressions involving the parameters s and t, and hence parametric equations of the form,
x = a(s,t),y = b(s,t) and z = c(s,t), where x = xi+yj+zk.

a)The plane through the points with coordinates (3, −1, 5) and (2, 8, −6) and parallel to the vector
8i−j+6k;

b)The plane containing the triangle ABC, where A, B and C have position vectors a = 3i − 4j + 2k,
b = 8i+9j−4k and c = 4i−3k;

3) Does the line through the point with coordinates (3, −5, 1) in the direction of the vector i + j − k meet the plane through the points with coordinates (3,−1,5) and (2,8,−6) and parallel to the vector 8i − j + 6k? If so, find the point(s) of intersection.

4 A rhombus is a parallelogram, all of whose sides have the same length,Show that the diagonals are perpendicular.
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You should understand that this is not a homework service nor is it a tutorial service. PLease either post some of your own work on this problem or explain what you do not understand about the question. What you have simply posted a long list of questions with nothing else. That is not acceptable.