Recently Active 3d And Vectors Questions

................................................ whcih formulae and results should we generally remeber in 3D +vectors chapter in both cartesian and vector form ?? ...

If direction cosines of a variable line in 2 adjacent points be l,m,n and l+δl,m+δm,n+δn .Show that small angle δθ between two positions is given by δθ2=δl2+δm2+δn2 ...

If the minimum distance of the point (1,1,1) from the plane x+y+z=1 measured perpendicular to the lines (x-a)/1 =( y-b)/2 =( z-c)/3 be ' l ' then the value of 21 l is ...... double integer answer ...

If AB = a, AD = b, AC = 2b+ 3c & the area of quadrialteral ABCD is β times the area of ||gm whose adjacent sides are a, b. find the value of β. Here, a represents vector a, AC represents vector AC. ...

How many max no. of planes can be drawn which are equidistant from 4 non coplanar points ???? Answer given is 7 ...but shouldnt it be infinite planes ??? because centroid of four points is equidistant from all points....and w ...

If the angle between a, b is twice the angle between a, c & b, c, then find the value of [a, b, c]. Here a, b, c represents unit vectors..... ...

If a, b, c are 3 non-coplanar unit vectors then, what is the value of [a b c]? a). 1 b). 1/2. c). 0 d) None of these. ...

The foot of perpendicular from the point (0, 0, 0) to the line of the intersection of the planes x + y + z = 4 & 2x + y + 3z = 1 is a point A.Find the equation of the line OA. ...

Vectors coincide with the edges of an arbitrary tetrahedron.Is it possible for the sum of these 6 vectors to equal the zero vector? ...

mod (vector a) =a & mod(vector b ) =b ..................then prove that {(vector a)/a^2 - (vector b)/b^2}^2 = {( vector a - vector b)/ab}^2 ...

prove that soln of eqn kr+rxa=b where k is non zero scaalr and a and b are non collinear vectors..is of form r= 1/(k2+a2) ( a.b/k a+kb+axb) ...

A parallelogram OABC ,s.t a,b,c respectively are position vectors of A,B,C wrt O (origin).A poin P is taken on BC which divides it in ration 2:1.Also line segment AP intersects the line bisecting angle O internally in point Q ...

\begin{Bmatrix} x+y=2\lambda & \\ x+\lambd^2y=\mu & \end{Bmatrix} system has infinite solns and the position vectors of two points A and B are given as (1,λ,2μ),(1,μ,λ2) respectively.AB is line segment divided by XY plane ...

Q1 graph of x2+y2=0 in 3D is ?? Q2 Locus of xy+yz=0 in 3D is ??? ...

unit vectors a and b are perpendicular to each other and unit vector c is inclined at angle θ to both a and b.If c=m(a+b)+n(axb) and m,n are real.Find range of θ I have found m=cosθ...and nothing else..help me out ...

Find vector which is orthogonal to vector 3i+2j+6k and is coplanar with 2i+j+k and i+j-k ...

There exists a plane f(a).x+f(0).y+f(c).z=1 which is passing through the point (0,1,1) where y=f(x) is a second degree polynomial which cuts the line x+y=1 at 2 distinct points x=1,x=c where c=rational number.It is also given ...

the vectors 2i-mj+3mk and (1+m)i - 2mj +k include an acute angle for what value of m??? ...

STATEMENT : (a.b)c - (a.c)b is perpendicular to a or b x c where (a.b)c - (a.c)b = a x (b x c) is it or (or) and ...

let a,b,c be three vectors such that they hav same mag. if |a-b|2+|b-c|2+|c-a|2=27 then a. a,b,c are coplanar b. a,b,c represent orthogonal triad of vectors c. a,b,c represents sides of a triangle (atleast in magnitude and di ...

WELCOME all tiitians this thread is open to all good Qs on Vectors & 3D & discussions on them PLZ dont post qs out of IIT JEE's level ...

ABCD ia a square of side length 6 2 units and EF is parallel to the square and is of length 12 2 units . The faces BCF and ADE are equilateral . The volume(in cubic unit) of the solid ABCDEF is equal to a. 384 b. 576 c.288 d. ...

How do u prove any linear eqn in x,y,z represent a plane? The reason I ask this is bcoz I'm having a fundamental problem in the proof itself! ...

if v1→=a*(b*c) ; v2→ =b*(c*a) ; & v3 → = c*(a*b) then : a) v1 +v2 + v3 is anull vector b)v1 ,v2 ,v3 can form side of a triangle c)v1 , v2 , v3 are coplanar d)v1 , v2 ,v3 are linearly dependent ...

1.the edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a cap , b cap, c cap. such that dotproduct of any of these unit vectors taken 2 at a time is 1/2. Find volume of parallelopiped. ...

Find the equation of the line passing through the point (4, -14, 4) and intersecting the line of intersection of the planes: 3x+2y-z = 5 and x-2y-2z = -1 at right angles. ...

Find the distance of the point P(-2, 3, -4) from the line x+2/3 = 2y+3/4 = 3z+4/5 measured parallel to the plane 4x+12y - 3z +1 = 0. ...

If a ,b and c are unit vectors,then show that 0≤ \left|\vec{a}-\vec{b} \right|^{2}+\left|\vec{b}-\vec{c} \right|^{2}+\left|\vec{c}-\vec{a} \right|^{2}\leq 9 \left|\vec{a}-\vec{b} \right|^{2}+\left|\vec{b}-\vec{c} \right|^{2 ...

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