Let \overrightarrow{ c } and \overrightarrow{ d } be vectors such that |\overrightarrow{ c }+\overrightarrow{ d } ∣=\sqrt{29} and \overrightarrow{ c } \times(2 î+3 ĵ+4 k̂)=(2 î+3 ĵ+4 k̂) \times \overrightarrow{ d }. If \lambda_1, \lambda_2 (\lambda_1>\lambda_2) are the possible values of (\overrightarrow{c}+\overrightarrow{d}) \cdot(-7 î+2 ĵ+3 k̂ ), then the equation K ^2 x^2+ ( K ^2-5 K+\lambda_1) x y+ (3 K+\frac{\lambda_2}{2}) y^2-8 x+12 y+\lambda_2=0 represents a circle, for K equal to : [21 Jan 2026 Shift 1]

JEE Main 21 Jan 2026 Shift 1 Paper Solved Paper

Section: Mathematics

Question : 19 of 75

Marks: +1, -0

Let

→

and

→

be vectors such that |

→

∣=√29 and

→

×(2î+3ĵ+4k̂)=(2î+3ĵ+4k̂)×

→

. If λ1,λ2(λ1>λ2) are the possible values of (

→

)⋅(−7î+2ĵ+3k̂), then the equation K2x2+(K2−5K+λ1)xy+(3K+‌

λ2

)y2−8x+12y+λ2=0 represents a circle, for K equal to :

[21 Jan 2026 Shift 1]

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