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Show that the poins whose position vecto...

Show that the poins whose position vectors are `4hat(i)+5hat(k),hat(i)+hat(j)+3hat(k)" and "-5hat(i)+3hat(j)-hat(k)` are collinear.

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If the points having position vectors hat(i)+bhat(j)+chat(k), 7hat(i)+2hat(j)+6hat(k) " and " 5hat(i)+2hat(j)+5hat(k) are collinear, find the values of b and c.

Given that the points with position vectors 12hat(i)-5hat(j), 10hat(i)+3hat(j) " and " xhat(i)+11hat(j) are collinear, find x.

If the vectors phat(i)-5hat(j)+6hat(k) " and " 2hat(i)-3hat(j)-qhat(k) are collinear, find p and q.

If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(k), 2hat(i)-hat(j)+hat(k) " and " hat(i)-3hat(j)-5hat(k) respectively. Show that ABC is right-angled triangle.

Show that the vectors 2hat(i)-hat(j)+hat(k), hat(i)-3hat(k)-5hat(k) " and " -2hat(i)+3hat(j)-4hat(k) are the sides of a right-angled triangle.

Find the area of triangle whose vertices have position vectors hat (i) + hat (j) + 2 hat (k) , 2 hat (i) + 2 hat (j) + 3 hat (k) and 3 hat (i) - hat (j) - hat (k)

The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) " and " 3hat(i)+6hat(j)-3hat(k) respectively. Show that the points form a right-angled triangle.

The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(k), hat(i)+2hat(j)+4hat(k) " and " 3hat(i)+10hat(j)-6hat(k) respectively. Show that the points A, B and C are collinear.

Find the value of lambda for which the three points with position vector 3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k , and4 hat i+5 hat j+lambda hat k are coplanar.

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Exercise 4A
  1. The equation of a line is given by x=by+c, z=ay+d, write it in cartes...

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

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

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

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

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

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

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

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

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

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  11. State which of the following statement is true ?

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

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

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

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

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

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

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

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

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  20. Find the angle between the following pair of lines vec(r)=(2hat(i)+...

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