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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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Show that the points A,B,C with 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 right angled triangle.Also,find the remaining angles of the triangle.

Show that the points A,B,C with position vectors (3hat(i)- 2 hat(j)+ 4hat(k)),(hat(i) + hat(j) +hat(k)) and (-hat(i)+ 4 hat(j)- 2 hat(k)) respectively are collinear.

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

Show that the four points A, B, C and D with position vectors 4hat(i)+5hat(j)+hat(k), -(hat(j)+hat(k)),3hat(i)+9hat(j)+4hat(k) and 4(-hat(i)+hat(j)+hat(k)) respectively are coplanar.

show that the points whose position vectors are (-2hat(i) +3hat(j) +5hat(k)) (hat(i)+2hat(j)+3hat(k)) " and " (7hat(i) -hat(k)) are collinear.

The values of a for which the points A,B, and C with position vectors 2hat i-hat j+hat k,hat i-3hat j-5hat k, and ahat i-3hat j+hat k respectively,are the vertices of a right-angled triangle with C=(pi)/(2) are

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

Show that the points A,B,C with position vectors 2hat ihat j+hat k,hat i35hat k and 3hat i4hat j4hat k respectively,are the vertices of a right-angled triangle.Hence find the area of the triangle.

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.

MODERN PUBLICATION-VECTOR ALGEBRA -Ncert File Question from Ncert Book (Exercise 10.3)
  1. Find the angle between two vectors veca and vecb with magnitudes sqrt(...

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  2. Find the angle between the vectors hat i-2 hat j+3 hat ka n d3 hat...

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  3. Find the projection of the vector hat i- hat jon the vector hat i+ ...

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  4. Find the projection of the vector hat i+3 hat j+7 hat kon the vector...

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  5. Show that each of the given three vectors is a unit vector: 1/7(2 hat...

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  6. find |veca|,|vecb| if (veca+vecb).(veca-vecb)=8 and |veca|=8|vecb|

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  7. Evaluate the product (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).

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  8. Find the magnitude of two vectors vec a\ a n d\ vec b having the sam...

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  9. Find |vec(x)|, if for a unit vector vec(a), (vec(x)-vec(a)).(vec(x)+ve...

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  10. If vectors veca = 2hati + 2hatj +3hatk,vec b=-hati+2hatj+hatk and vec ...

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  11. Show that |vec(a)|vec(b)+|vec(b)|vec(a) is perpendicular to |vec(a)|v...

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  12. If vec a\ dot\ vec a=0 and vec a\ dot\ vec b=0, then what can be c...

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  13. If vec a ,\ vec b ,\ vec c are unit vectors such that vec a+ vec b...

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  14. If either vec a= vec0\ or\ vec b= vec0\ t h e n\ vec adot vec b= ve...

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  15. If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) ...

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  16. Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10 , 1)are colli...

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

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  18. If vec a is a non zero vector a magnitude ' a^(prime)\ a n d\ lambda ...

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