If the plane passes through three collinear points \((x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)\) then which of the following is true?(a) \(x_1 y_1 z_1+x_2 y_2 z_2+x_3 y_3 z_3\)=0(b) \(\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}\)=0(c) \(\begin{vmatrix}x_1\\y_2\\z_3\end{vmatrix}\)=0(d) \(x_1 x_2 x_3+y_1 y_2 y_3+z_1 z_2 z_3=0\)The question was asked in an interview for internship.My question comes from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12

If the plane passes through three collinear points \((x_1,y_1,z_1),(x_

1.	If the plane passes through three collinear points \((x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)\) then which of the following is true?(a) \(x_1 y_1 z_1+x_2 y_2 z_2+x_3 y_3 z_3\)=0(b) \(\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}\)=0(c) \(\begin{vmatrix}x_1\\y_2\\z_3\end{vmatrix}\)=0(d) \(x_1 x_2 x_3+y_1 y_2 y_3+z_1 z_2 z_3=0\)The question was asked in an interview for internship.My question comes from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Answer» Right ANSWER is (b) \(\BEGIN{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}\)=0 The explanation: If the THREE points are collinear, then they will be in a straight LINE and hence the determinant of the three points will be zero. i.e.\(\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}\)=0

Discussion

No Comment Found

Related InterviewSolutions

What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are parallel to each other?(a) a1a2 . b1b2 . c1c2 = 0(b) a1a + b1b + c1c = 0(c) a1a2 + b1b2 – c1c2 = 0(d) a1a2 + b1b2 – c1c2 = 0The question was posed to me during a job interview.The doubt is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Find the angle between x + 2y + 7z + 2 = 0 and (2, 4, 6).(a) 69.69(b) 84.32(c) 66.92(d) 83.25I got this question during an online exam.The question is from Three Dimensional Geometry topic in chapter Three Dimensional Geometry of Mathematics – Class 12
The condition \(\frac {a}{a1} = \frac{b}{b1} = \frac{c}{c1}\) is for a plane and a line are _____ to each other.(a) perpendicular(b) parallel(c) differential(d) tangentialI have been asked this question by my college professor while I was bunking the class.This intriguing question comes from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Find the angle between 2x + 3y – 2z + 4 = 0 and (2, 1, 1).(a) 38.2(b) 19.64(c) 89.21(d) 29.34The question was asked in examination.The origin of the question is Three Dimensional Geometry in chapter Three Dimensional Geometry of Mathematics – Class 12
A plane and a line having an angle of 90 degrees between them are called _____(a) Orthogonal(b) Tangential(c) Normal(d) ParallelI had been asked this question in semester exam.My doubt stems from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
What is the relation between the plane ax + by + cz + d = 0 and a1, b1, c1 the direction ratios of a line, if the plane and line are perpendicular to each other?(a) \(\frac {a1}{b1} = \frac{a2}{c1} = \frac{c2}{b2}\)(b) \(\frac {a1}{a2} = \frac{b1}{c2} = \frac{c1}{b2}\)(c) \(\frac {a}{a1} = \frac{b}{b1} = \frac{c}{c1}\)(d) \(\frac {c1}{a2} = \frac{b1}{b2} = \frac{a1}{c2}\)I got this question in an online interview.I'm obligated to ask this question of Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Find k for the given plane x + 2y + kz + 2 = 0 and directional ratios of a line (8, 3, 2), if they are parallel to each other.(a) 21(b) -17(c) 12(d) -7This question was addressed to me in homework.My question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
Find the angle between the planes 5x + 2y + 3z + 1 = 0 and (1, 1, -2).(a) 30.82(b) 3.43(c) 11.23(d) 7.54The question was asked during an online exam.Question is taken from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12
The plane 5x + y + kz + 1 = 0 and directional ratios of a line (3, -1, 1) are parallel, find k.(a) 4(b) -14(c) 6(d) -8I got this question in an international level competition.This key question is from Three Dimensional Geometry in portion Three Dimensional Geometry of Mathematics – Class 12
The condition a1a + b1b + c1c = 0 is for a plane and a line are _____ to each other.(a) integral(b) parallel(c) perpendicular(d) concentricThis question was addressed to me in an online quiz.The doubt is from Three Dimensional Geometry topic in portion Three Dimensional Geometry of Mathematics – Class 12

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment