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Evaluate the following determinates |{...

Evaluate the following determinates
`|{:(1+2hati,1-hati),(1+hati,1-2hati):}|`

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Find the angle between the following pairs of lines : (i) vecr=2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and veck=7hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Compute the magnitude of the following vectors : veca=hati+hatj+k,vecb=2hati-7hatj-3hatk,vecc=(1)/(sqrt(3))hati+(1)/(sqrt(3))hatj-(1)/(sqrt(3))hatk

Compute the magnitude of the following vectors : (i) vec(a)=2hati+3hatj+sqrt(3)hatk (ii) vec(b)=3hati-4hatk (iii) vec( c )=hati+hatj-4hatk

Find the Cartesian equation of the following planes : (a) vecr.(hati+hatj-hatk)=2 (b) vecr.(2hati+3hatj-4hatk)=1 (c) vecr.((s-2t)hati+(3-t)hatj+(2s+t)hatk)=15

Find the vector equation of the plane containing the lines vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) .

Find the area of the parallelogy whose diagonals are determined the vectors 2hati+hatk and hati+hatj+hatk .

Find the equation of the plane through the line of intersection of vecr.(2hati-3hatj+4hatk)=1 and vecr.(hati-hatj)+4=0 and perpendicular to vecr.(2hati-hatj+hatk)+8=0

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

The value of lamda for which the four points 2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk and hati-lamdahatj+6hatk are coplanar.

Find the angle between the vectors 2hati-hatj+hatk and 3hati+4hatj-hatk .

KUMAR PRAKASHAN-DETERMINANTS -Practice Work
  1. Evaluate the following determinates |{:(1,omega),(omega,-omega):}| w...

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  2. Evaluate the following determinates |{:(sin10^@,-cos10^@),(sin80^@, ...

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  3. Evaluate the following determinates |{:(1+2hati,1-hati),(1+hati,1-2h...

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  4. Evaluate the following determinates |{:(logab,1),(1,logba):}|

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  5. Evaluate the following determinates |{:(-1,3,4),(1,9,12),(9,9,12):}|

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  6. Evaluate the following determinates |{:(0,1,sectheta),(tantheta,-sec...

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  7. If |{:(x+1,x-1),(x-3,x+2):}|=|{:(4,-1),(1,3):}| then find x

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  8. If |{:(1,2,x),(1,1,1),(2,1,-1):}|=0 then find x.

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  9. If |{:(4,x),(-3,5):}|=8 then find x.

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  10. If |{:(m,-2),(5,2m):}|=|{:(5,-4),(5,3):}| then find m

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  11. If |{:(x,1,2),(1,0,3),(5,-1,4):}|=0 then find x

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  12. Using the property of determinants and without expanding prove the fol...

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  13. Using the property of determinants and without expanding prove the fol...

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  14. Using the property of determinants and without expanding prove the fol...

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  15. Using the property of determinants and without expanding prove the fol...

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  16. Using the property of determinants and without expanding prove the fol...

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  17. Using the properties of determinants, solve the following for x |{:(...

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  18. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

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  19. Using the properties of determinants, prove the following |{:((b+c)^...

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  20. Using the properties of determinants, prove the following |{:((x-2)^...

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