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Show that the vectors vec(a)=hat(i)-2hat...

Show that the vectors `vec(a)=hat(i)-2hat(j)+3hat(k) vec(b)=-2i+3hat(j)-4hat(k)vec( c) =hat(i) -3 hat(j) +5hat(k)` are coplanar.

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`[vec(a),vec(b),vec( c)]=|(1,-2,3),(-2,3,-4),(1,-3,5)|=0 therefore vec(a), vec(b) , vec (c )` are coplanar.
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SUBHASH PUBLICATION-VECTOR ALGEBRA -TWO MARKS/THREE MARKS QUESTIONS WITH ANSWERS
  1. Evaluate the product (3vec(a)-5vec(b)).(2vec(a)+7vec(b)).

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  2. Find the magnitude of two vectors vec(a) and vec(b) having the same ma...

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  3. Find |x|, if for a unit vector a, (vec(x)-vec(a)).(vec(x)+vec(a))=12.

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  4. If a=2hat(i)+2hat(j)+3hat(k),b=hat(i)+2hat(j)+hat(k) and c=3hat(i)+hat...

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  5. Show that |a|b+|b| a is perpendicular to |a|b-|b| a for any two non- z...

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  6. If a,b,c are unit vectors such that a+b+c=0, then find the value of a....

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  7. If either a=0,b=0, then a.b=0. But the converse need not to be true . ...

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  8. If the vertices A,B,C of a triangle ABC have position vectors (1,2,3),...

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  9. Show that the points A(1,2,7),B(2,6,3) and C(3,10,-10 are collinear.

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  10. Show that the vectors 2hat(i)-hat(j)+hat(k),hat(i)-3hat(j). And 3hat(i...

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  11. Find |vec(a)xxvec(b)|, if a=hat(i) -7hat(j)+7k and b=3hat(i)-2hat(j)+2...

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  12. Find a unit vector perpendicular to each of the vectors (veca+vecb) an...

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  13. If a unit vector hat(a), makes angles (pi)/(3) with hat(i),(pi)/(4) wi...

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  14. Show that (vec(a)-vec(b))xx(vec(a)+vec(b))=2 (vec(a)xxvec(b)).

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  15. Find lambda and u, if (2hat(i)+6hat(j)+27hat(k))xx(hat(i)+lambdahat(j)...

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  16. Given that a.b=0 and axxb=0. What can you conclude about the vectors a...

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  17. Prove that [vec(a)+vec(b),vec(b)+vec( c) , vec( c) +vec(a)] =2 [vec(a)...

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  18. Prove that [vec(a),vec(b),vec( c) +vec(d)]=[vec(a),vec(b),vec( c)] +[v...

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  19. Find the volume of the parallelopiped whose cotermius edges are 2hat(i...

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  20. Show that the vectors vec(a)=hat(i)-2hat(j)+3hat(k) vec(b)=-2i+3hat(j)...

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