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Vector equation of the plane r = hati-ha...

Vector equation of the plane `r = hati-hatj+ lamda(hati +hatj+hatk)+mu(hati – 2hatj+3hatk)` in the scalar dot product form is

A

`rcdot(5i-2j+3k)=7`

B

`rcdot(5i2j-3k)=7`

C

`rcdot(5i-2j-3k)=7`

D

`rcdot(5i+2j+3k)=7`

Text Solution

Verified by Experts

The correct Answer is:
(c)
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Find the vector equation of the following plane in scalar product form: vecr=hati-hatj+lambda(hati+hatj+hatk)+mu(hati-2hatj+3hatk)

Find the vector equation in scalar product form of the plane vecr=2hati-hatj+lambda(hati+2hatj+3hatk)+mu(2hati-hatj-3hatk) .

Find the angle between the vectors hati-2hatj+3hatk and 3hati - 2hatj + hatk

Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

Check whether the lines vecr=hati+hatj-hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+hatk) intersect or not.

If the vectors 2hati-hatj+hatk,hati+2hatj-3hatk and 3hati+ahatj+5hatk are coplanar, the prove that a=-4.

The projection of the vector 2hati+3hatj+2hatk on the vector hati+2hatj+hatk

Show that the vectors hati-hatj-hatk,2hati+3hatj+hatk and 7hati+3hatj-4hatk are coplanar.

Using scalar triple product prove that the four points whose position vectors are given by the vectors , 4hati-2hatj+hatk , 5hati+hatj+6hatk , 2hati+2hatj-5hatk and 3hati+5hatj are coplanar.

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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Single Option Correct Type Questions)
  1. Which of the following pairs of linear equations are consistent ? Obta...

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  2. A parallelopiped is formed by planes drawn through the points (1, 2, 3...

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  3. Vector equation of the plane r = hati-hatj+ lamda(hati +hatj+hatk)+mu(...

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  4. Find the shortest distance between the lines whose equations are : vec...

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  5. Consider the plane (x,y,z)= (0,1,1) + lamda(1,-1,1)+mu(2,-1,0) The dis...

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  6. The value of a for which the lines (x-2)/(1)=(y-9)/(2)=(z-13)/(3) and ...

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  7. For the line (x-1)/1=(y-2)/2=(z-3)/3, which one of the following is ...

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  8. Given planes P1:cy+bz=x P2:az+cx=y P3:bx+ay=z P1, P2 and P3 pass...

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  9. The lines (x-2)/(1)=(y-3)/(1)=(z-4)/(-k) and (x-1)/(k)=(y-4)/(2)=(z-5)...

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  10. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z...

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  11. The line which contains all points (x, y, z) which are of the form (x,...

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  12. If the position vectors of the points A,B and C be hati+hatj,hati-hatj...

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  13. Find the equation of plane passing through the line of intersection o...

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  14. A straight line is given by r=(1+t)i+3tj+(1-t)k, where tinR. If this l...

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  15. Find the distance of the point (-1, -5, -10) from the point of interse...

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  16. What is the Next Prime Number after 7 ?

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  17. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

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  18. The orthogonal projection A' of the point A with position vector (1, 2...

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  19. The equation of the line passing through (1, 1, 1) and perpendicular t...

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  20. Find the value of x Equation is x+7=4

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