This type of question, asked 5 times: 25 Jul 2022, 27 Jul 2022, 31 Jan 2023, 8 Apr 2023, 11 Apr 2023. All 5 questions below, oldest first.
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Question 1
25 Jul 2022
90
The line of shortest distance between the lines 0x−2=1y−1=1z and 2x−3=2y−5=1z−1 makes an angle of cos−1(272) with the plane :ax−y−z=0,(a>0). If the image of the point (1,1,−5) in the plane P is (α,β,γ), then α+β−γ is equal to
Question 2
27 Jul 2022
165
If the line of intersection of the planes ax+by=3 and ax+by+cz=0,a>0 makes an angle 30∘ with the plane y−z+2=0, then the direction cosines of the line are :
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Question 3
31 Jan 2023
85
Let θ be the angle between the planes P1:r⋅(++2k)=9 and P2:r⋅(2−+k)=15. Let L be the line that meets P2 at the point (4,−2,5) and makes an angle θ with the normal of P2. If α is the angle between L and P2, then (tan2θ)(cot2α) is equal to
Question 4
8 Apr 2023
162
For a,b∈Z and ∣a−b∣≤10, let the angle between the plane P:ax+y−z=b and the line l:x−1=a−y=z+1 be cos−1(31). If the distance of the point (6,−6,4) from the plane P is 36, then a4+b2 is equal to
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Question 5
11 Apr 2023
178
Let the line l:x=−21−y=λz−3,λ∈R meet the plane P:x+2y+3z=4 at the point (α,β,γ). If the angle between the line l and the plane P is cos−1(145), then α+2β+6γ is equal to
