INTRODUCTION TO THREE DIMENSIONAL GEOMETRY - Pyqs

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Q1
If the coordinates of a point \(P\) are \((2, -3, 5)\), then the distance of \(P\) from the \(xy\)-plane is
(Exam: IIT-JEE Year: 1998)
(A) \(2\)
(B) \(3\)
(C) \(5\)
(D) \(\sqrt{38}\)
Q2
The coordinates of a point on the \(x\)-axis at a distance \(7\) from the origin can be
(Exam: AIEEE Year: 2004)
(A) \((0, 7, 0)\)
(B) \((7, 0, 0)\)
(C) \((0, 0, 7)\)
(D) \((7, 7, 0)\)
Q3
The distance between the points \(A(1, 2, 3)\) and \(B(4, 6, 3)\) is
(Exam: NEET Year: 2016)
(A) \(5\)
(B) \(6\)
(C) \(\sqrt{34}\)
(D) \(\sqrt{25}\)
Q4
The coordinates of the foot of the perpendicular from the origin to the \(yz\)-plane are
(Exam: IIT-JEE Year: 2001)
(A) \((0, 0, 0)\)
(B) \((1, 0, 0)\)
(C) \((0, 1, 0)\)
(D) \((0, 0, 1)\)
Q5
A point \(P(x, y, z)\) lies on the \(xz\)-plane if
(Exam: BITSAT Year: 2012)
(A) \(x = 0\)
(B) \(y = 0\)
(C) \(z = 0\)
(D) \(x = y\)
Q6
The distance of the point \((3, -4, 12)\) from the origin is
(Exam: KVPY Year: 2014)
(A) \(13\)
(B) \(5\)
(C) \(12\)
(D) \(\sqrt{29}\)
Q7
The locus of a point equidistant from the \(xy\)-plane and \(yz\)-plane is
(Exam: IIT-JEE Year: 2005)
(A) \(x = y\)
(B) \(y = z\)
(C) \(|x| = |z|\)
(D) \(|x| = |y|\)
Q8
The point which is equidistant from all the three coordinate axes is
(Exam: AIIMS Year: 2010)
(A) \((1, 1, 1)\)
(B) \((1, 2, 3)\)
(C) \((2, 1, 0)\)
(D) \((0, 1, 1)\)
Q9
The coordinates of the midpoint of the line joining \((2, -4, 6)\) and \((-2, 4, 10)\) are
(Exam: JEE Main Year: 2019)
(A) \((0, 0, 8)\)
(B) \((2, 0, 8)\)
(C) \((0, 2, 8)\)
(D) \((0, 0, 16)\)
Q10
The coordinates of a point on the \(y\)-axis at a distance \(5\) from the origin are
(Exam: State CET Year: 2015)
(A) \((5, 0, 0)\)
(B) \((0, 5, 0)\)
(C) \((0, 0, 5)\)
(D) \((5, 5, 0)\)
Q11
If \(A(1, 1, 1)\), \(B(2, 3, 4)\), and \(C(3, 5, 7)\) are collinear, then
(Exam: IIT-JEE Year: 2007)
(A) \(\overrightarrow{AB} = \overrightarrow{BC}\)
(B) \(\overrightarrow{AB}\) is parallel to \(\overrightarrow{BC}\)
(C) \(|AB| = |BC|\)
(D) The points lie on the \(xy\)-plane
Q12
The distance between the points \((a, 0, 0)\) and \((0, b, 0)\) is
(Exam: BITSAT Year: 2013)
(A) \(|a-b|\)
(B) \(\sqrt{a^2 + b^2}\)
(C) \(a + b\)
(D) \(\sqrt{ab}\)
Q13
The point \((0, 0, 0)\) is called
(Exam: NEET Year: 2018)
(A) Unit point
(B) Origin
(C) Axial point
(D) Reference point
Q14
The plane \(x = 0\) represents
(Exam: IIT-JEE Year: 1995)
(A) \(xy\)-plane
(B) \(yz\)-plane
(C) \(xz\)-plane
(D) A line
Q15
The distance of the point \((0, 3, 4)\) from the \(x\)-axis is
(Exam: JEE Main Year: 2020)
(A) \(3\)
(B) \(4\)
(C) \(5\)
(D) \(\sqrt{7}\)
Q16
The coordinates of the point symmetric to \(A(2, -3, 4)\) about the \(xy\)-plane are
(Exam: IIT-JEE Year: 2003)
(A) \((2, -3, -4)\)
(B) \((-2, -3, 4)\)
(C) \((2, 3, 4)\)
(D) \((-2, 3, -4)\)
Q17
A point lies in the third octant if
(Exam: NEET Year: 2017)
(A) \(x>0, y>0, z>0\)
(B) \(x<0, y<0, z<0\)
(C) \(x>0, y<0, z>0\)
(D) \(x<0, y>0, z<0\)
Q18
The distance of the point \((4, 3, 0)\) from the \(y\)-axis is
(Exam: BITSAT Year: 2011)
(A) \(3\)
(B) \(4\)
(C) \(5\)
(D) \(\sqrt{7}\)
Q19
The coordinates of the centroid of the triangle with vertices \((1, 2, 3)\), \((3, 2, 1)\), and \((2, 4, 6)\) are
(Exam: IIT-JEE Year: 2008)
(A) \((2, 8, 10)\)
(B) \((2, \frac{8}{3}, \frac{10}{3})\)
(C) \((\frac{8}{3}, 2, \frac{10}{3})\)
(D) \((\frac{2}{3}, \frac{8}{3}, \frac{10}{3})\)
Q20
A point \(P\) is equidistant from the planes \(x=0\) and \(y=0\). Its locus is
(Exam: KVPY Year: 2015)
(A) \(x=y\)
(B) \(x=-y\)
(C) \(|x|=|y|\)
(D) \(x+y=0\)
Q21
The distance between the points \((1, -1, 2)\) and \((-2, 3, -2)\) is
(Exam: JEE Main Year: 2021)
(A) \(5\)
(B) \(\sqrt{33}\)
(C) \(6\)
(D) \(7\)
Q22
The point which lies on both the \(xy\)-plane and the \(yz\)-plane is
(Exam: IIT-JEE Year: 1997)
(A) \((0, 0, z)\)
(B) \((x, 0, 0)\)
(C) \((0, y, 0)\)
(D) \((0, 0, 0)\)
Q23
The coordinates of a point dividing the line joining \((2, 2, 2)\) and \((4, 6, 8)\) internally in the ratio \(1:3\) are
(Exam: NEET Year: 2019)
(A) \((\frac{5}{2}, 3, \frac{7}{2})\)
(B) \((\frac{7}{2}, 5, \frac{13}{2})\)
(C) \((3, 4, 5)\)
(D) \((\frac{10}{4}, \frac{14}{4}, \frac{20}{4})\)
Q24
The point \((0, -5, 0)\) lies on
(Exam: State Engineering Exam Year: 2016)
(A) \(x\)-axis
(B) \(y\)-axis
(C) \(z\)-axis
(D) \(xz\)-plane
Q25
The locus of a point whose distance from the \(xy\)-plane is constant \(k\) is
(Exam: IIT-JEE Year: 2004)
(A) \(x=k\)
(B) \(y=k\)
(C) \(z=\pm k\)
(D) \(x+y+z=k\)
Q26
The distance of the point \((1, 2, 2)\) from the \(z\)-axis is
(Exam: BITSAT Year: 2014)
(A) \(1\)
(B) \(2\)
(C) \(\sqrt{5}\)
(D) \(3\)
Q27
The coordinates of the point symmetric to \((3, 4, -5)\) about the origin are
(Exam: IIT-JEE Year: 1999)
(A) \((-3, -4, 5)\)
(B) \((3, -4, 5)\)
(C) \((-3, 4, -5)\)
(D) \((3, 4, 5)\)
Q28
The point \((x, y, z)\) is at equal distance from the three coordinate planes if
(Exam: Olympiad Year: 2013)
(A) \(x=y=z\)
(B) \(|x|=|y|=|z|\)
(C) \(x+y+z=0\)
(D) \(xyz=1\)
Q29
The number of octants in three dimensional geometry is
(Exam: NEET Year: 2020)
(A) \(4\)
(B) \(6\)
(C) \(8\)
(D) \(12\)
Q30
The coordinates of the origin in three dimensional geometry are
(Exam: State CET Year: 2014)
(A) \((1, 1, 1)\)
(B) \((0, 0, 0)\)
(C) \((-1, -1, -1)\)
(D) \((0, 1, 0)\)
Q31
The distance between \((0, a, 0)\) and \((0, 0, b)\) is
(Exam: IIT-JEE Year: 2002)
(A) \(a+b\)
(B) \(|a-b|\)
(C) \(\sqrt{a^2+b^2}\)
(D) \(\sqrt{ab}\)
Q32
A point lies on the \(xz\)-plane if its
(Exam: JEE Main Year: 2018)
(A) \(x=0\)
(B) \(y=0\)
(C) \(z=0\)
(D) \(x=z\)
Q33
The distance of the point \((2, 0, 0)\) from the \(yz\)-plane is
(Exam: BITSAT Year: 2010)
(A) \(0\)
(B) \(1\)
(C) \(2\)
(D) \(\sqrt{2}\)
Q34
The midpoint of the line joining \((a, 0, 0)\) and \((0, b, 0)\) is
(Exam: IIT-JEE Year: 1996)
(A) \((\frac{a}{2}, \frac{b}{2}, 0)\)
(B) \((a, b, 0)\)
(C) \((\frac{a+b}{2}, 0, 0)\)
(D) \((0, 0, \frac{a+b}{2})\)
Q35
The locus of a point moving such that its distance from the origin is constant is
(Exam: Olympiad Year: 2016)
(A) A plane
(B) A sphere
(C) A line
(D) A cone
Q36
The distance of \((0, 4, 3)\) from the \(x\)-axis is
(Exam: NEET Year: 2015)
(A) \(4\)
(B) \(3\)
(C) \(5\)
(D) \(7\)
Q37
A point lies in the first octant if
(Exam: JEE Main Year: 2017)
(A) Only one coordinate is positive
(B) Exactly two coordinates are positive
(C) All coordinates are positive
(D) All coordinates are negative
Q38
The coordinates of a point on the \(z\)-axis are
(Exam: State Board Year: 2013)
(A) \((x, y, 0)\)
(B) \((0, y, z)\)
(C) \((0, 0, z)\)
(D) \((x, 0, z)\)
Q39
The distance between \((1, 2, 3)\) and the origin is
(Exam: IIT-JEE Year: 2000)
(A) \(6\)
(B) \(\sqrt{14}\)
(C) \(3\)
(D) \(\sqrt{6}\)
Q40
The plane \(z=0\) is known as
(Exam: NEET Year: 2014)
(A) \(yz\)-plane
(B) \(xz\)-plane
(C) \(xy\)-plane
(D) Axis plane
Q41
The point \((2, -3, 0)\) lies in
(Exam: BITSAT Year: 2015)
(A) \(xy\)-plane
(B) \(yz\)-plane
(C) \(xz\)-plane
(D) \(z\)-axis
Q42
The distance of the point \((0, 0, 7)\) from the origin is
(Exam: JEE Main Year: 2016)
(A) \(0\)
(B) \(7\)
(C) \(\sqrt{7}\)
(D) \(49\)
Q43
The reflection of \((x, y, z)\) in the \(yz\)-plane is
(Exam: IIT-JEE Year: 2006)
(A) \((x, -y, z)\)
(B) \((-x, y, z)\)
(C) \((x, y, -z)\)
(D) \((-x, -y, -z)\)
Q44
The locus of a point equidistant from the axes is
(Exam: Olympiad Year: 2012)
(A) \(x=y=z\)
(B) \(|x|=|y|=|z|\)
(C) \(x+y+z=0\)
(D) \(xyz=0\)
Q45
The coordinates of the foot of the perpendicular from \((3, 4, 5)\) to the \(xy\)-plane are
(Exam: IIT-JEE Year: 1994)
(A) \((3, 4, 0)\)
(B) \((0, 0, 5)\)
(C) \((3, 0, 5)\)
(D) \((0, 4, 5)\)
Q46
The distance of the point \((1, 1, 1)\) from the plane \(x=0\) is
(Exam: NEET Year: 2021)
(A) \(0\)
(B) \(1\)
(C) \(\sqrt{2}\)
(D) \(\sqrt{3}\)
Q47
A point whose coordinates satisfy \(x=y=z\) lies on
(Exam: IIT-JEE Year: 2009)
(A) A plane
(B) A line
(C) A sphere
(D) An axis
Q48
The distance between \((a, a, a)\) and the origin is
(Exam: BITSAT Year: 2016)
(A) \(a\)
(B) \(\sqrt{3a}\)
(C) \(\sqrt{3}a\)
(D) \(3a\)
Q49
The point \((0, 0, -5)\) lies on
(Exam: State CET Year: 2018)
(A) \(xy\)-plane
(B) \(yz\)-plane
(C) \(xz\)-plane
(D) \(z\)-axis
Q50
The distance between the points \((1, 0, 0)\) and \((0, 1, 0)\) is
(Exam: IIT-JEE Year: 1993)
(A) \(1\)
(B) \(\sqrt{2}\)
(C) \(2\)
(D) \(\sqrt{3}\)

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