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If a line has a vector equation, vecr=2h...

If a line has a vector equation, `vecr=2hati +6hatj+lambda(hati-3hatj)` then which of the following statements holds good ?

A

the line is parallel to `2hati +6hatj`

B

the line passes through the point `3hati+3hatj`

C

the line passes through the point `hati+9hatj`

D

the line is parallel to xy plane

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B, C, D
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Let P_(1) denote the equation of a plane to which the vector (hati+hatj) is normal and which contains the line whose equation is vecr=hati+hatj+veck+lamda(hati-hatj-hatk)andP_(2) denote the equation of the plane containing the line L and a point with position vector j. Which of the following holds good? (a) The equation of P_(1)" is"x+y=2. (b) The equation of P_(2)" is "vecr.(hati-2hatj+hatk)=2. (c) The acute angle the P_(1)andP_(2)" is "cot^(-1)(sqrt3) . (d) The angle between the plnae P_(2) and the line L is tan^(-1)sqrt3 .

The line whose vector equation are vecr =2 hati - 3 hatj + 7 hatk + lamda (2 hati + p hatj + 5 hatk) and vecr = hati - 2 hatj + 3 hatk+ mu (3 hati - p hatj + p hatk) are perpendicular for all values of gamma and mu if p equals :

The lines with vector equations are, vecr_(1)=3hati+6hatj+lambda(-4hati+3hatj+2hatk) and vecr_(2)=-2hati+7hatj+mu(-4hati+hatj+hatk) are such that :

The lines with vector equations are, vecr_(1)=3hati+6hatj+lambda(-4hati+3hatj+2hatk) and vecr_(2)=-2hati+7hatj+mu(-4hati+hatj+hatk) are such that :

If vecr = hati + hatj + lamda( 2 hati + hatj + 4 hatk ) and vecr (hati + 2 hatj - hatk)=3 are the equations of a line and a plane respectively then which of the following is true ?

Find the vector equation of line passing through the point (-1, 2, 1) and parallel to the line vecr=2hati+3hatj-hatk+lamda(hati-2hatj+hatk) . Also , find the distance between these lines .

The co-ordinates of the point P on the line vecr =(hati +hatj + hatk)+lambda (-hati +hatj -hatk) which is nearest to the origin is

Find the shortest distance between the lines l_(1)and l_(1) whose vector equations are vecr=(hati+hatj) + lambda (3hati + 4hatj - 2hatk) …(i) and vecr=(2hati+3hatj) + mu (6hati + 8hatj - 4hatk) …(ii)

The equation of the plane containing the line vecr=hati+hatj+lamda(2hati+hatj+4hatk) is

Find the shortest distance between the two lines whose vector equations are given by: vecr=hati+2hatj+3hatk+lamda(2hati+3hatj+4hatk) and vecr=2hati+4hatj+5hatk+mu(3hati+4hatj+5hatk)

VK JAISWAL ENGLISH-VECTOR & 3DIMENSIONAL GEOMETRY-Exercise-2 : One or More than One Answer is/are Correct
  1. If equation of three lines are : (x)/(1)=(y)/(2)=(z)/(3), (x)/(2)=...

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  2. If veca=hati+6hatj+3hatk, vecb=3hati+2hatj+hatk and vec c=(alpha+1)hat...

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  3. Consider the lines : L(1): (x-2)/(1)=(y-1)/(7)=(z+2)/(-5) L(2):x-4...

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  4. Let hata, hatb and hatc be three unit vectors such that hata=hatb+(h...

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  5. The value(s) of mu for which the straight lines vecr=3hati-2hatj-4hatk...

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  6. If hati xx [ (veca-hatj) xxhati]+ hatj xx [(veca - hatk)xx hatj] +hatk...

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  7. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to (a)[veca...

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  8. If veca,vecb,vecc & vecd are position vector of point A,B,C and D resp...

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  9. veca and vecc are unit vectors and |vecb|=4 the angle between veca and...

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  10. Consider the lines x=y=z and line 2x+y+z-1=0=3x+y+2z-2, then

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  11. If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd, wh...

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  12. If (veca xx vecb) xx (vec c xx vecd)=h veca+k vecb=r vec c+s vecd, wh...

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  13. Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a h...

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  14. The volume of a right triangular prism ABCA(1)B(1)C(1) is equal to 3 c...

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  15. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc=...

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  16. If a line has a vector equation, vecr=2hati +6hatj+lambda(hati-3hatj) ...

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  17. Let M,N, P and Q be the mid points of the edges AB, CD, AC and BD resp...

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  18. The solution vectors vecr of the equation vecr xx hati=hatj+hatk and v...

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  19. The lines with vector equations are, vecr(1)=3hati+6hatj+lambda(-4hat...

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