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Show that the vectors hat(i)-3hat(j)+4...

Show that the vectors
`hat(i)-3hat(j)+4hat(k),2hat(i)-hat(j)+2hat(k)and 4hat(i)-7hat(j)+10hat(k)` are coplanar.

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Verified by Experts

Let`vec(a)=hat(i)-3hat(j)+4hat(k),vec(b)=2hat(i)-hat(j)+2hat(k)and vec(c)=4hat(i)-7hat(i)+10hat(k)`.`:. [vec(a)vec(b)vec(c)]=|(1,-3,4),(2,-1,2),(4,-7,10)|=|(1,-3,4),(0,5,-6),(0,5,-6)||(R_(2)rarrR_(2)-2R_(1)),(R_(3)rarrR_(3)-4R_(1))|`
`=(-30+30)=0`.
Hence, the given vectors are coplanar.
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RS AGGARWAL-PRODUCT OF THREE VECTORS-Objective Questions
  1. Show that the vectors hat(i)-3hat(j)+4hat(k),2hat(i)-hat(j)+2hat(k)a...

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  2. Find a unit vector in the direction of vec a=2 hat i-\ 3 hat j+6 hat ...

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  3. Write the direction cosines of the vector -2 hat i+ hat j-5 hat k

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  4. If A(1,2,-3) and B(-1,-2,1) are the two given points in space then fi...

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  5. If a vector makes angle alpha,beta,gamma with OX, OY and OZ respective...

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  6. The vector (cosalphacosbeta) hat i+(cosalphas inbeta) hat j+(s inalpha...

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  7. What is the angle which the vector (hat(i)+hat(j)+sqrt(2)hat(k)) makes...

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  8. If vec(a) and vec(b) are vectors such that |vec(a)|=sqrt(3), |vec(b)|=...

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  9. If vec(a) and vec(B) are two vectors such that |vec(a)|=|vec(b)|=sqrt(...

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

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  11. If vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k))...

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  12. If vec(a)=(hat(i)+2hat(j)-3hat(k)) and vec(b)=(3hat(i)-hat(j)+2hat(k))...

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  13. If vec(a)=(2hat(i)+4hat(j)-k^(2)) and vec(b)=(3hat(i)-2hat(j)+lambda h...

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  14. What is the projection of vec(a)=(2hat(i)-hat(j)+hat(k)) on vec(b)=(h...

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  15. If |veca + vecb| = |veca - vecb|, then

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  16. If vec(a) and vec(b) are mutually perpendicular unit vectors then (3ve...

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  17. If the vectors vec(a)=3hat(i)+hat(j)-2hatk and vec(b)=hat(i)+lambda ha...

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  18. If theta is the angle between two unit vectors hat(a) and hat(b) then ...

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  19. If vec(a)=(hat(i)-hat(j)+2hat(k)) and vec(b)=(2hat(i)+3hat(j)-4hat(k))...

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  20. If vec(a)=(hat(i)-2hat(j)+3hat(k)) and vec(b)=(hat(i)-3hat(k)) then |v...

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  21. If | vec a|=2,\ | vec b|=7\ a n d\ vec axx vec b=3 hat i+2 hat j+6 ha...

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