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Prove that the four points having positi...

Prove that the four points having position vectors are coplanar: `2 hat i- hat j+ hat k ,\ hat i-3 hat j-5 hat k\ a n d\ 3 hat i-4 hat j-4 hat k`

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The correct Answer is:
`x=-1, y=1`
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Prove that the four points having position vectors are coplanar: 2hat i-hat j+hat k,hat i-3hat j-5hat k and 3hat i-4hat j-4hat k

Prove that the four points having position vectors are coplanar: hat i+hat j+hat k,2hat i+3hat j-hat k and -hat i-2hat j+2hat k

Prove that the four points having position vectors are non-coplanar: hat i+2hat j+3hat k,2hat i+hat j+3hat k and hat i+hat j+hat k

Prove that the four points having position vectors are non-coplanar; 3hat i+hat j-hat k,2hat i-hat j+7hat k and 7hat i-hat j+23hat k

Show that the points whose position vectors are as given below are collinear: 2hat i+hat j-hat k,3hat i-2hat j+hat k and hat i+4hat j-3hat k3hat i-2hat j+4hat k,hat i+hat j+hat k and -hat i+4hat j-2hat k

Prove that the points having position vectors hat i+2hat j+3hat k,3hat i+4hat j+7hat k,quad -3hat i-2hat j-5hat k are collinear.

Show that the points whose position vectors are 5 hat i+5 hat k ,\ 2 hat i+ hat j+3 hat k\ a n d-4 hat i+3 hat j- hat k are collinear.

Show that the point A , B and C with position vectors vec a =3 hat i - 4 hat j -4 hat k = 2 hat i j + hat k and vec c = hat i - 3 hat j - 5 hat k , respectively from the vertices of a right angled triangle.

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

Show that each of the following triads of vectors are coplanar: vec a= hat i+2 hat j- hat k , vec b=3 hat i+2 hat j+7 hat k , vec c=5 hat i-6 hat j+5 hat k vec a=-4 hat i-6 hat j-2 hat k , vec b=- hat i+4 hat j+3 hat k , vec c=8 hat i- hat j+3 hat k hat a= hat i-2 hat j+3 hat k , vec b=-2 hat i+3 hat j-4 hat k , vec c= hat i-3 hat j+5 hat k

MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. Show that the points, A, B and C having position vectors (2hat(i)-hat(...

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  2. The position vectors of A, B, C are 2hat(i)+hat(j)-hat(k), 3hat(i)-2ha...

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  3. Prove that the four points having position vectors are coplanar: 2 hat...

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  4. Show that the found points A ,B ,C ,D with position vectors vec a , v...

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  5. Find the magnitude of each of the two vectors veca and vec b having th...

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  6. If vec(a) and vec(b) are perpendicular vectors such that |vec(a)+vec(b...

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  7. Find the projection of the vector hat i+3 hat j+7 hat k on the vector...

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  8. Find lambda, when the projection of vec a=lambda hat i+ hat j+4 hat k...

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  9. If vec a and vec b are two unit vectors such that vec a+ vec b is a...

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  10. Find | vec x| , if for a unit vector vec a ,\ ( vec x-\ vec a)dot( v...

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  11. If ā,b,c are three vectors such that |veca |= 5, |vecb| = 12 and | ...

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  12. If vec(a) , vec(b) and vec(c ) be three vectors such that vec(a) + vec...

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  13. Three vectors vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3h...

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  14. If vec a ,\ vec b ,\ vec c are three mutually perpendicular vectors...

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  15. Find a vector vec a of magnitude 5sqrt(2) making an angle pi/4 with x-...

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  16. Let vec(A)=4hat(i)+5hat(j)-hat(k), vec(b)=hat(i)-4hat(j)+5hat(k) and v...

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  17. If with reference to a right handed system of mutually perpendicula...

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  18. If vectors vec a\ a n d\ vec b\ are such that | vec a|=3,\ | vec b|...

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  19. If 'theta' is the angle between the vectors : vec(a)=hat(i)+2hat(j)+3h...

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  20. Find 'lambda' and 'mu' if : (hat(i)+3hat(j)+9hat(k))xx(3hat(i)-lam...

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