Jee Practice Mathematics Vectors 3d Geometry

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📐Chapter Practice

Vectors & 3D Geometry — JEE Practice

30 practice questions across 2 topics. Filter by difficulty, solve topic-wise MCQs, and review detailed solutions.

2 Topics30 Questions

Vectors(15 Qs)

easy (5)

Q1If a⃗ = 2î + 3ĵ, |a⃗| =Q2The dot product a⃗·b⃗ = |a⃗||b⃗|cos θ. If θ = 90°:Q3î·î =Q4î × ĵ =Q5Two vectors are parallel if a⃗ × b⃗ =

medium (5)

Q1The projection of a⃗ on b⃗ is:Q2|a⃗×b⃗| equals:Q3Section formula: point dividing A and B in ratio m:n is:Q4Scalar triple product [a⃗ b⃗ c⃗] gives:Q5If a⃗ = î+ĵ and b⃗ = î-ĵ, then a⃗·b⃗ =

hard (5)

Q1The area of triangle with vertices A, B, C is:Q2Vector equation of a line through a⃗ and parallel to b⃗ is:Q3Distance of point P from plane r⃗·n̂ = d is:Q4The shortest distance between two skew lines r⃗=a⃗₁+λb⃗₁ and r⃗=a⃗₂+μb⃗₂ is:Q5Equation of plane through 3 points A, B, C: [r⃗-a⃗, b⃗-a⃗, c⃗-a⃗] = 0 represents:

3D Coordinate Geometry(15 Qs)

easy (5)

Q1Distance between (1,2,3) and (4,6,3) is:Q2Direction ratios of a line joining (0,0,0) and (1,1,1) are:Q3The equation of xy-plane is:Q4The general equation of a plane is:Q5The distance of origin from plane 2x + 2y + z = 9 is:

medium (5)

Q1Direction cosines satisfy:Q2Angle between two planes a₁x+b₁y+c₁z=d₁ and a₂x+b₂y+c₂z=d₂:Q3The line (x-1)/2 = (y-2)/3 = (z-3)/4 passes through:Q4Two planes are perpendicular if:Q5The image of (1,2,3) in the plane x+y+z = 6 is:

hard (5)

Q1The distance between parallel planes 2x+y-2z=5 and 2x+y-2z=8 is:Q2The foot of perpendicular from (1,1,1) to line (x-1)/2 = y/1 = (z+1)/3 is found by:Q3Equation of plane through line of intersection of P₁=0 and P₂=0:Q4Coplanarity condition for lines r⃗=a⃗₁+λb⃗₁, r⃗=a⃗₂+μb⃗₂:Q5The angle between a line with DR (a,b,c) and plane Ax+By+Cz=D is:

More Mathematics Chapters

Sets, Relations & Functions

15 Qs

Complex Numbers

15 Qs

Quadratic Equations

15 Qs

Permutations & Combinations

15 Qs

Binomial Theorem

15 Qs

Matrices & Determinants

15 Qs

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