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Find the angle between the pair of lines...

Find the angle between the pair of lines
`r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k))`
`r=5hat(i)-4hat(k)+mu(3hat(i)+2hat(j)+6hat(k))`

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Verified by Experts

The correct Answer is:
`cos^(-1)(19)/(21)`
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Find the angle between the pairs of line r=3hat(i)+2hat(j)-4hat(k)+lambda(hat(i)+2hat(j)+2hat(k)) and hat(r)=5hat(i)-2hat(j)+mu(3hat(i)+2hat(j)+6hat(k)) .

Find the angle between the pair of lines given by vec r=3hat i+2hat j-4hat k+lambda(hat i+2hat j+2hat k) and vec r=5hat i-2hat j+mu(3hat i+2hat j+6hat k)

The angle between the line r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k)) and the plane r*(2hat(i)-hat(j)+hat(k))=4 is

vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

Find the angle between the lines vec r=3hat i+2hat j-4hat k+lambda(hat i+2hat j+2hat k) and vec r=(5hat j-2hat k)+mu(3hat i+2hat j+6hat k)

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by r=(3hat(i)+8hat(j)+3hat(k))+lambda(3hat(i)-hat(j)+hat(k)) and r=(-3hat(i)-7hat(j)+6hat(k))+mu(-3hat(i)+2hat(j)+4hat(k)) .

Consider the following 3lines in space L_1:r=3hat(i)-hat(j)+hat(k)+lambda(2hat(i)+4hat(j)-hat(k)) L_2: r=hat(i)+hat(j)-3hat(k)+mu(4hat(i)+2hat(j)+4hat(k)) L_3:=3hat(i)+2hat(j)-2hat(k)+t(2hat(i)+hat(j)+2hat(k)) Then, which one of the following part(s) is/ are in the same plane?

ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find the angle between the pair of lines r=3hat(i)+2hat(j)-4hat(k)+l...

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  2. Consider a pyramid OPQRS located in the first octant (xge0, yge0, zge0...

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  3. Let P be the image of the point (3, 1, 7) with respect to the plane x...

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  4. From a point P(lambda, lambda, lambda), perpendicular PQ and PR are dr...

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  5. Two lines L(1) : x=5, (y)/(3-alpha)=(z)/(-2) and L(2) : x=alpha, (y)/(...

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  6. A line l passing through the origin is perpendicular to the lines 1:...

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  7. Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=...

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  8. If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/...

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  9. If the distance between the plane Ax-2y+z=d and the plane containing ...

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  10. Read the following passage and answer the questions. Consider the line...

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  11. Read the following passage and answer the questions. Consider the line...

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  12. Read the following passage and answer the questions. Consider the line...

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  13. Consider three planes P(1):x-y+z=1 P(2):x+y-z=-1 and " "P...

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  14. Consider the planes 3x-6y-2z=15a n d2x+y-2z=5. Statement 1:The parame...

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  15. If the image of the point P(1,-2,3) in the plane, 2x+3y-4z+22=0 measur...

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  16. The distance of the point (1, 3, -7) from the plane passing through th...

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  17. The distance of the point (1,-5,""9) from the plane x-y+z=5 measured a...

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  18. If the line, (x-3)/2=(y+2)/(-1)=(z+4)/3 lies in the place, l x+m y-z=9...

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  19. The disatance of the point (1, 0, 2) from the point of intersection of...

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  20. The equation of the plane containing the line 2x-5y+z=3, x+y+4z=5 and ...

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  21. The angle between the lines whose direction cosines satisfy the equ...

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