MEDIUM
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If P is a point on the line parallel to the vector 2i^-3j^-6k^ and passing through the point A whose position vector is i^+2j^-2k^ and AP=21, then the position vector of P can be

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Important Questions on Three Dimensional Geometry

MEDIUM
A point P lies on a line through Q(1,-2,3) and is parallel to the line x1=y4=z5. If P lies on the plane 2x+3y-4z+22=0, then segment PQ equals
MEDIUM

Directions: Each of the following sentences in this section has a blank space and four words or group of words given after the sentence. Select the word or group of words you consider most appropriate for the blank space and indicate your response on the Answer Sheet accordingly.

Every rash driver becomes a ____ killer.

EASY
The equation of the line passing through the point (2,3,-4) and perpendicular to the XOZ plane is λR
EASY
The line x-23=y+12=z-1-1, intersects the curve xy=c2,z=0 if c is equal to
HARD
The lines x-12=y+12=z-14 and x-31=y-62=z1 intersect each other at point
HARD
Let the position vectors of two points P and Q be 3i^-j^+2k^ and i^+2j^-4k^, respectively. Let R and S be two points such that the direction ratios of lines PR and QS are 4,-1,2 and -2,1,-2, respectively. Let lines PR and QS intersect at T. If the vector TA is perpendicular to both PR and QS and the length of vector TA is 5 units, then the modulus of a position vector of A is :
EASY
The parametric equations of the line passing through A3, 4, -7, B1,-1, 6 are λR
MEDIUM
Two lines in a three-dimensional system are given as (x-1)2=(y-2)3=(z-3)4 and (x-4)5=(y-1)2=z. Their point of intersection is
EASY

Two sentences are given below and you are required to find the correct sentence which combines both the sentences.

Which is the correct combination of the given two sentences?

He is too tired. He could not stand.

EASY
Let P be the point of intersection of two lines x+101=y-217=z+115 and x-15=y-469=z3. If Q be the point (-10,21,-11); then PQ is equal to
MEDIUM

In the following sentence, a blank space with four options is given. Select whichever preposition or determiner you consider the most appropriate for the blank space.

These are the good rules to live _____.

EASY
The Cartesian equation of the line passing through the points (1,-1,2) and 7,0,5 is
HARD
For real numbers α and β0, if the point of intersection of the straight lines x-α1=y-12=z-13 and x-4β=y-63=z-73 lies on the plane x+2y-z=8, then α-β is equal to :
MEDIUM
If the lines x-12=y+13=z-14 and x-31=y-k2=z1 intersect, then k equals
MEDIUM
The distance of the point (1,2,3) from the plane x+y+z=2 measured parallel to the line x+1-1=y-2=z-31 is
EASY
The equation of the line joining the points (-3, 4, 11 and (1, -2, 7) is
HARD
The direction ratios of a normal to a plane are (3, 12, 4). Through which of the following points the plane passes if origin is at a distance of 2 units from this plane?
HARD
Let 3i^+j^-k^ be the position vector of a point B. Let A be a point on the line which is passing through B and parallel to the vector 2i^-j^+k^. If BA=18, then the position vector of A is
MEDIUM
A plane P meets the coordinate axes at A,B and C respectively. The centroid of ABC is given to be 1,1,2. Then the equation of the line through this centroid and perpendicular to the plane P is :
MEDIUM
If line x-12=y+13=z-14 and x-31=y-λ2=z1 intersect each other, then λ=..