Math Assignment Class VIII | Square & Square Root

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Question 1: A line makes angle 𝜶, 𝛃, 𝛾 with x-axis, y-axis, z-axis. Then find cos2𝜶, cos2𝛃, cos2𝛾 ? Ans. 1 -1 |
Question 2:
Write vector
equation of the line: |
Question 3: Find the Cartesian equation of the
line which passes through the point (-2, 4, -5) and is parallel to the line Hint: Two parallel lines have same direction ratio. Ans. 3 |
Question 4: Find angle between pair of lines
Ans 4: 90o |
Question 5: Find the point on the given line at
a distance 3√2 from the point (1, 2, 3). Ans 5: |
Question 6:
Find the length and
foot of perpendicular drawn from the point (2, -1, 5) on the line Ans 6: |
Question 7: Find the shortest distance between the lines :- Ans 7: |
Question 8: Find the equation of a line passing through the point P(2,-1,3) and perpendicular to the lines:
Ans 8: |
Question 9: Show that the following lines are intersecting, also find their point of intersection.
Ans 9: (-1, -6, -12) |
Question 10: Show that the following lines are coplanar. |
Question 11: Find the distance of the given plane from the origin: Ans 11 : 2/7 |
Question 12:
Find the angle
between the planes Ans 12 |
Question 13:
Find the equation of
the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which
contains the line of intersection of planes x + 2y + 3z - 4 = 0 and 2x + y -
z + 5 = 0 Ans 13: 51x + 15y - 50z + 173 = 0 , λ = -29/7 |
Question 14:
Find the equation of
the plane passing through the point (-1, 3, 2) and perpendicular to each of
the plane x + 2y + 3z = 5 and 3x + 3y + z = 0. Ans 14: 7x - 8y + 3z + 25 = 0 |
Question 15:
Find the equation of
the plane through (2, 1, -1) and (-1, 3, 4) and perpendicular to the
plane x -2y + 4z = 10. Ans 15: 18x + 17y + 4z -49 = 0 |
Question 16: Find image p' of point p having position vector
Ans. 16: Image (-3, 5, 2), Length = 2√6 |
Question 17: Find the distance of the point (1, -2,
3) from the plane x - y + z = 5 measured parallel to the line Ans 17: λ = 1/7, AB = 1 |
Question 18:
Find the distance of
the point (-2, 3, -4) from the given line measured ∥ to the plane 4x + 12y - 3z + 1 = 0 Ans 18: λ = 2/3 , Point is (4, 5/2, 2), Distance = 17/2 |
Question 19:
Find the equation of
the plane passing through the point P(4, 6, 2) and the point of intersection
of the plane x + y - z = 8 and the line Ans 19 |
Question 20: Find the vector equation of the plane through the line of intersection of planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0. Hence find whether plane thus obtained contains the line Ans 20 : |
Question 21: Find the angle between the following line and plane :
Ans 21: 0o |
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