Frequent 3d And Vectors Questions

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Prove the formula for vector triple product.. ...

What is component of vector? Plzz explain in simple manner ...

If a line lies on a plane can we say that the line is parallel to that plane? ...

Points whose position vectors are a+b,a-b,a+kb are collinear for: (a) Only one integral value of k (b) All integral values of k (C) None of these ...

Points x and y lie on the side QR and RS of a parallelogram PQRS such that QX =2XR and RY=3YS.Thus the value of u such that the diagonal PR meets line XY at Z and PZ=u PR is ?Characters in bold face denote vectors. ...

If \vec{a},\vec{b},\vec{c} are non-co-planar unit vectors such that \vec{a} x ( \vec{b} x \vec{c} ) = (\vec{b}+\vec{c})/(\sqrt{2}) , \vec{b} and \vec{c} are non parallel, then find the angle between \vec{a} and \vec{b} . ...

Can anyone explain reciprocal system of vectors? Its the only topic I am not understanding properly! :/ ...

In a Triangle ABC, the bisector of angle A meets the opposite side at D. Using vectors Prove that BD : DC = c : b. (AIEEE Question Doubt) ...

Q.1. In a Triangle ABC, the bisector of angle A meets the opposite side at D. Using vectors Prove that BD : DC = c : b. Q.2. The vector (-1,1,1) bisects the angle between the vectors C(x,y,z) and (3,4,0). determine a unit vec ...

1. In the isosceles triangle ABC, \left|\vec{AB} \right|=\left|\vec{BC} \right|=8 , a point E divides AB internally in the ratio 1:3, then the cosine of the angle between \vec{CE} & \vec{CA} is ( where \left| \vec{CA}\right|= ...

ANGLE BETWEEN THE LINES WHOSE DIRECTION COSINES ARE GIVEN BY EQUATION 3l + m + 5n=0 6mn - 2nl + 5ml=0 is ...

a detalied explanation for what a nilpotent matrix is...i need it... ps---NISHANT SIR, help... ...

a rigid body rotates with constant angular velocity w about the line whose vector equation is r=lambda(i+2j+2k). the speed of the particle at the instant it passes through the point with p.v. 2i+3j=5k is a) w√2 b) 2w c)w/∠...

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got it got it sorry thanks everyone! ...

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the number of straight lines that are equally inclined to the three dimensional co-ordinate axis ,is ...

the angle b/w the lines whose direction cosines satisfy the equations l + m + n = 0 , l2 + m2 - n2 = 0 is given by ...

*Image* In the soln its given that no three planes can meet at two distinct points. But we can have infinite number of planes through a given line. isnt it? Plese clarify ...

the eqn. of the plane passing through the intersection of the plane 2x-5y+z=3 and x+y+4z=5 and parallel to the plane x+3y+6z=1 is x+3y+6z=k where k is. ...

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Guys having a problem to find the equation of the line of shortest distance between 2 skew lines. take for an example between ........ x+4/4 = y-2/-2 = z-3/0 and x-5/5 = y-3/3 = z/0 please show the working.......(ans- x/0 = y ...

I already knw da answers to the followin questions. I am interested 2 knw da solution.Pls solve dem guys. I) |(a x b).c| = |a||b||c| ,if (1)a.b=b.c=0 (2)b.c=c.a=0 (3)c.a=a.b=0 (4)a.b=b.c=c.a=0 II) If b and c are two non-colli ...

1) if A(1,-1,3) B(2,1,-2) C(-5,2,-6) are the vertices of a triangle ABC , then the length of internal angular bisctor of angle A is?? 2)the median AD of triangle ABC is bisected at E and BE meets AC at F then AF:FC ??? 3)if x ...

Find the angle between the lines x-2/3 = y+1/-2, z=2 and x-1/1 = 2y+3/3 = z+5/2 This question came in my 12th board and I lost 1 mark in it [2] Again this question came while taking coaching. I have one doubt z=2 is a plane.. ...

if the direction ratios of two lines are given by 3lm -4ln + mn = 0 and l + 2m + 3n = 0 , find the angles between them ...

1) Given vectors A, B and C forms a triangle such that A = B + C. find a,b,c and d such that the area of the triangle is 5 6 where, A=ai + bj + ck B=di + 3j + 4k C=3i + j - 2k well the sum is very easy but i am not getting an ...

If O be the circumcentre and O' be te orthocentre of ΔABC then prove that (i) OA + OB + OC = OO' (ii) O'A + O'B + O'C = 2 O'O (iii) OAsin2A + OBsin2B + OCsin2C = 0 bold lines signify vectors and 0 signifies nul vector!! plea ...

If a,b,c,d are unit vectors such that (a x b) . (c x d) =1 and a . c=1/2.....then A) a,b,c are non coplanar B) b,c,d are non coplanar C) b,d are non parallel D) a,d are parallel and b,c are parallel ...