Recently Active 3d And Vectors Questions

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 ...

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just for practice 1)Find an equation of the line through the point A (4,5,5) which meets the line (x-11)/3 = (y+8)/-1 = z-4 at right angles. ...

If axb=c bxc=a then find relation b/w a,b,c I have got some ans..but i dont have answer key..so tell me ur answer..... ...

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 ...

1. There are 2 vectors, one in the horizontal direction and other is inclined at an angle of 600 with the vertical.The resultant is in vertical direction and has magnitude P units.The 2 vectors are: a)P,2P b)P,P√3 c)2P,P√ ...

If a1 and a2 are 2 non-collinear unit vectors and if |a1 + a2| =√3, then the value of(a1 -a2).(2a1 +a2) is: a)2 b) 3/2 c) 1/2 d)1 Plz show with steps as i dont know how to start.. ...

The sum and difference of two vectors are perpendicular to each other.What is the magnitude of individual vectors? ...

1.if \vec{a} \times \vec{b} = \vec{c} \times \vec{d} and \vec{a} \times \vec{c} = \vec{b} \times \vec{d} then prove that (\vec{a} -\vec{d})\left| \right| (\vec{b}-\vec{c}) . 2.A line makes \alpha ,\beta ,\gamma and \delta wit ...

1. if A and B are two events such that P(A∩B)=P(A) then P(A/B)=1 or P(B/A)=1?? 2. tan x dy/dx-(sec2x)y= sin x here I.F. is cot x or tan x? 3. dy/dx+y=tan x .. here I.F. is elogx?? ...

if a,b and c are unit vectors, then *Image* does not exceed? ...

The value of sine of angle between the vectors 2 i - j + 3 k and 3 i + 2 j + k is A stupid qs I know But if i take dot product i am getting cos A = 1/2 so sin A = root 3/2 But if i take cross product i am getting sin A =1 /2 ...

1. An arc AC of a circle subtends a right angle at the centre O. The point B divides the arc in the ratio 1:2 . If and OB =b then find OC in terms of a and b. ...

Question 1 If \vec{a} , \vec{b} , \vec{c} be such that | \vec{a} + \vec{b} + \vec{c} |=1, \vec{c} = \lambda \vec{a} x \vec{b} and |a|= 1/ 2 , |b|= 1/ 3 , |c|= 1/ 6 then the angle between \vec{a} and \vec{b} is: A) Î /6 B) Î / ...

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Q17. Find the image of the point (1,6,3) about the "plane"(???) x = (y-1)/2 = (z-2)/3 <- How is this a plane?? My working -: *Image* *Image* ...

Prove that line x=ay+b, z=cy+d and x= a'y+b', z=c'y+d' are perpendicular if aa'+cc'=-1( edited) ...

1. ∫1/sin2x+cos2xdx = a) -2cot2x+c b) tanx-cotx+c c) 9+(sec2x)/2 d) 3-tan2x/2 e) (3-sec2x)/2 f) (tan2x/2)-5 2. If vectors a+b=vector c then vector a x b = a) c x a b) a x c c) b x c d) c x b 3. If the direction ratio of a l ...

Q1. A and B are points with coordinates (2,1,3) and (4,-2,5) respectively. 2x+y-z=3 is the equation of a plane (A) Line AB is parallel to the plane (B) AB meets the plane at (0,4,1) (c) The plane divides AB externally in the ...

Q. What is the formula for volume of a tetrahedron whose vertices are given by the vectors a, b, c, d Q. How to decide whether a system of planes can form a prism or not? ...

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A non-zero vector a i s parallel to the line of intersection of plane P1 determined by i+j , i - 2j and plane P2 determined by vector 2i + j ,3i + 2k , then angle between a and vector i - 2j +2k is (A)Î /4 (B) Î /2 (C) Î /3 ( ...

Q) A Square ABCD of diagonal 2a is folded along the diagonal AC so that the planes DAC and BAC are at right angles. The shortest distance between DC and AB is a) √2a b) 2/3 a c) 2/√5 a d) √3/2 a ...

Q1. The image of the plane x-y+z+6=0 with respect to the plane mirror 4x-2y-6z+14=0 is ax+by+cz+6=0, then the value of cos-1a + cos-1b+ cos-1c is ...

The image of the plane x-y+z+6=0 with respect to the plane mirror 4x-2y-6z+14=0 is ax+by+cz+6=0, then the value of cos-1a+cos-1b+cos-1c is equal to A)pi B)2 pi C)3 pi/2 D) 3 pi ...

1. if DA=a, AB=b and CB=ka where k>0 and X,Y are the mid pts of DB and AC respt. such that |a|=17 and |XY|=4 then k is a)8/17 b)9/17 c)25/17 d)4/17 2. ax(bxc), b(cxa), cx(axb) are a)linearly dependent b)equal c)parallel d) ...

Let first line be x = y = z, second line be x=y/2=z/3 and third line is passing through (1, 1, 1). Area of triangle formed by these three lines is √6 unit, and point of intersection of third line with second line is (a, b, ...

A) 3 dice are rolled and 3 numbers a,b,c are selected, then probability that the 3 planes : ax+by+cz=0 bx+cy+az=0 cx+ay+bz=0 form 1) exactly 1 line is 0 2) a point is 105/108 3) a prism is 0 4) whole space is 1 (Multiple Choi ...

in ΔABC,O,N,G,O' are circumcentre,nine point centre,centroid and orthocentre .AL and BM are perpendiculars from A nad B on sides BC and CA.Let AD be the median and OD is perpenndicular to side BC and R be circumradius of ΔA ...