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Let the position vectors of the points P...

Let the position vectors of the points P, Q and R are respectively given by `2hat(i)+5hat(j)-8hat(k), " "-3hat(j)+6hat(k)" and "-3hat(i)+2hat(j)+3hat(k)`. IF PQRS is a parallelogram, find the equation of QS in certesian and vector form.

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The correct Answer is:
`(x)/(-1)=(y+3)/(13)=(z-6)/(-17);vec(r)=(-3hat(j)+6hat(k))+t(-hat(i)+13hat(j)-17hat(k))`
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If the vectors phat(i)-5hat(j)+6hat(k) " and " 2hat(i)-3hat(j)-qhat(k) are collinear, find p and q.

In a DeltaABC , right angled at the vertex A, If the positive vectors of A, B and C are respectively 3hat(i) + hat(j) - hat(k), -hat(i) + 3hat(j) + phat(k) and 5hat(i) + qhat(j) - 4hat(k) , then the point (p,q) lies on a line-

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. Find the equation of the line which passes through (1,2,-4) and (4,-5,...

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  2. The equation of a line is given by x=by+c, z=ay+d, write it in cartes...

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  3. Let the position vectors of the points P, Q and R are respectively giv...

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  4. Show that the poins whose position vectors are 4hat(i)+5hat(k),hat(i)+...

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  5. Find the points on the line (x+2)/(3)=(y+1)/(2)=(z-3)/(2) at a distanc...

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  6. Show that the line joining the points P and Q with position vectors ve...

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  7. (i) Find the vector equation of a line passing through a point with po...

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  8. The angle between the straight lines (x-4)/(2)=(y-5)/(0)=(z-6)/(0) and...

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  9. The angle between the straight lines x=5,y=4t+5,z=4t+3 and (x-5)/(5)=(...

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  10. The straight lines (x-x(1))/(l(1))=(y-y(1))/(m(1))=(z-z(1))/(n(1))" an...

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  11. The straight lines (x)/(a(1))=(y)/(b(1))=(z)/(c(1)) and (x-2)/(a(2))=(...

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  12. State which of the following statement is true ?

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  13. The angles between the lines (x-5)/(2)=(y-3)/(2)=(z)/(0) and x=5,y=8,z...

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  14. The angle between the lines(x-5)/(1)=(y-1)/(0)=(z-9)/(0) and 2x-1=5-2y...

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  15. The lines (x)/(1)=(y)/(2)=(z)/(3) and (x-1)/(-2)=(y-2)/(-4)=(3-z)/(6) ...

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  16. Find the angle between the lines (x-5)/(7)=(y+2)/(-5)=(z-9)/(1) and (x...

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  17. Find the angle between the lines (x-7)/(2)=(y-6)/(3)=(z+2)/(-4) and (2...

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  18. The cartesian equation of a line AB is (3-x)/(1)=(y+2)/(-2)=(z-5)/(4)....

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  19. Find the equation of a line passing through the point (1,2,3) and para...

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  20. Find the angle between the following pair of lines vec(r)=(3hat(i)+...

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