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12

Q1. Show that the points (-2, 3 , 5 ) , ( 1, 2 , 3 ) and ( 7, 0 , -1 ) are collinear.

Solution

Q2. Find the co-ordinates of the point which divide the line segment joining the point (1,-2,3) and (3,4,-5) in the ratio 2 : 3 externally.

Solution

Q3. Find the ratio in which the line segment joining the points (5,9,11) and (7,11,-9) is divided by the YZ plane

Solution

Q4. Name the octant in which the following points lie : (i) (4,-2,-5) (ii) (-4,2,-5)(iii) (1,2,3)

Solution

(i) VIIIth Octant (ii) VIth Octant (iii) Ist Octant
Q5. A point is in the YZ plane. What is the value of the x-coordinate?

Solution

Since the point lies in the YZ plane the value of x-cordinate is zero.
Q6. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, -1)

Solution

Q7. If the origin is the centroid of the triangle PQR with vertices P(2a,2,6) Q(-4,3b,-10) and R(8,14,2c), then find the values of a,b,c

Solution

Q8. The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (4,-6,4) and (-2,8,-7)respectively, find the coordinates of the point C.

Solution

Q9. F i n d space t h e space c o minus o r d i n a t e s space o f space a space p o i n t space o n space t h e space y minus a x i s space a t space a space d i s tan c e space 5 square root of 2 space f r o m t h e space p o i n t space A left parenthesis 3 comma 2 comma 5 right parenthesis

Solution

A n y space p o i n t space o n space y space a x i s space i s space g i v e n space b y space left parenthesis 0 comma y comma 0 right parenthesis D i s tan c e space o f space t h i s space p o i n t space f r o m space left parenthesis 3 comma 2 comma 5 right parenthesis space i s space 5 square root of 2 rightwards double arrow left parenthesis 0 minus 3 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared plus left parenthesis 0 minus 5 right parenthesis squared equals 50 rightwards double arrow y squared minus 4 y minus 12 equals 0 rightwards double arrow y equals 6 comma negative 2 S o space t h e space c o minus o r d i n a t e s space a r e space left parenthesis 0 comma 6 comma 0 right parenthesis space a n d space left parenthesis 0 comma negative 2 comma 0 right parenthesis
Q10. A point P is at a distance of 6 units from the origin on the Z axis. Write the coordinates of P

Solution

The coordinates of P are left parenthesis 0 comma 0 comma plus-or-minus 6 right parenthesis
Q11. Find the distance between the points P(1, -3, 4) and Q (- 4, 1, 2).

Solution



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