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Show that the points, A, B and C having position vectors `(2hat(i)-hat(j)+hat(k)), (hat(i)-3hat(j)-5hat(k))` and `(3hat(i)-4hat(j)-4hat(k))` respectively are the vertices of a rightangled triangle. Also, find the remaining angles of the triangle.

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The correct Answer is:
`=sqrt(35)`
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MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. Prove that if vec(u)=u(1)hat(1)hat(i)+u(2)hat(j) and vec(v)=v(1)hat(i)...

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  2. Find the value of ' p ' for which the vectors 3 hat i+2 hat j+9 hat k\...

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  3. Show that the points, A, B and C having position vectors (2hat(i)-hat(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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