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Class XII 3 – Dimensional Geometry

Q97: Find the vector and Cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines (𝒙−𝟏)/𝟏=(𝒚−𝟐)/𝟐=(𝒛−𝟑)/𝟑 and 𝒙/(−𝟑)=𝒚/𝟐=𝒛/𝟓.

Previous Videos related to this chapter are mentioned in the below link:
Q15: The x-coordinate of a point on the line joining the points P (2,2,1) and Q (5,1,-2) is 4. Find its z-coordinate.:    • The x-coordinate of a point on the line jo...  
Q16: Find the direction cosines of the line:    • Find the direction cosines of the line: (x...  
(x-1)/2=-y=(z+1)/2
Q17: Find the direction cosines of the line:    • Find the direction cosines of the line:(𝟒−...  
(4-x)/2=y/6=(1-z)/3
Q18: If the equation of a line AB is (3-x)/(-3)=(y+2)/(-2)=(z+2)/6, then, find the direction cosines of a line parallel to AB.:    • If the equation of a line AB is (𝟑−𝒙)/(−𝟑)...  
Q22: The equation of line is 5x-3=15y+7=3-10z. Write the direction cosines of the line.:    • The equation of line is 𝟓𝒙−𝟑=𝟏𝟓𝒚+𝟕=𝟑−𝟏𝟎𝒛. ...  
Q23: If equation of line is r ⃗=(i ̂+j ̂ )+λ(3i ̂+4j ̂+6k ̂ ) then find the direction cosine of this line:    • If equation of line is 𝑟 ⃗=(𝑖 ̂+𝑗 ̂ )+𝜆(3𝑖...  
Q27: If the Cartesian equation of a line is (3-x)/5=(y+4)/7=(2z-6)/4, write the vector equation for the line.:    • If the Cartesian equation of a line is (𝟑−...  
Q31: Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3i ̂+2j ̂-2k ̂.:    • Find the equation of the line which passes...  
Q33: Find the equation of the line in vector and in Cartesian form that passes through the point with position vector 2i ̂-j ̂+4k ̂ and is in the direction of i ̂+2j ̂-k ̂:    • Find the equation of the line in vector an...  
Q36: Find the vector equation of a line passing through a point with position vector 2i ̂-j ̂+k ̂, and parallel to the line joining the points -i ̂+4j ̂+k ̂ and i ̂+2j ̂+2k ̂. Also, find the Cartesian equivalent of this equation.:    • Find the vector equation of a line passing...  
Q45: The Cartesian equation of a line is 6x-2=3y+1=2z-2. Find the direction cosines of the line. Write down the Cartesian and vector equations of line passing through (2,-1,-1) which is parallel to the given line.:    • The Cartesian equation of a line is 𝟔𝒙−𝟐=𝟑...  
Q50: Find the equation of line passing through (1,1,2) and (2,3,–1):    • Find the equation of line passing through ...  
CONCEPT: ANGLE BETWEEN TWO LINES:    • CONCEPT: ANGLE BETWEEN TWO LINES  
Q56: Find the angle between the lines r ⃗=3i ̂+2j ̂-4k ̂+λ(i ̂+2j ̂+2k ̂) and r ⃗=(5i ̂-2j ̂ )+μ(3i ̂+2j ̂+6k ̂).:    • Find the angle between the lines 𝒓 ⃗=𝟑𝒊 ̂+...  
Q60 Find the angle between the following pair of lines:
x/2=y/2=z/1 & (x-5)/4=(y-2)/1=(z-3)/8:    • Find the angle between the following pair ...  
Q62: Find the angle between following pairs of lines. (-x+2)/(-2)=(y-1)/7=(z+3)/(-3) and (x+2)/(-1)=(2y-8)/4=(z-5)/4 and check whether the lines are parallel or perpendicular:    • Find the angle between following pairs of ...  
Q65: Find the value of p, so that the lines l_1:(1-x)/3=(7y-14)/p=(z-3)/2 and l_2:(7-7x)/3p=(y-5)/1=(6-z)/5 are perpendicular to each other. Also find the equation of a line passing through a point (3,2,–4) and parallel to line l_1:    • Find the value of p, so that the lines l_1...  




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