jee-main 2022 Q77

jee-main · India · session2_28jul_shift2 Vectors Introduction & 2D Angle or Cosine Between Vectors

Let $S$ be the set of all $a \in R$ for which the angle between the vectors $\vec { u } = a \left( \log _ { e } b \right) \hat { i } - 6 \hat { j } + 3 \hat { k }$ and $\vec { v } = \left( \log _ { e } b \right) \hat { i } + 2 \hat { j } + 2 a \left( \log _ { e } b \right) \hat { k } , ( b > 1 )$ is acute. Then $S$ is equal to
(1) $\left( - \infty , - \frac { 4 } { 3 } \right)$
(2) $\Phi$
(3) $\left( - \frac { 4 } { 3 } , 0 \right)$
(4) $\left( \frac { 12 } { 7 } , \infty \right)$

Let $S$ be the set of all $a \in R$ for which the angle between the vectors $\vec { u } = a \left( \log _ { e } b \right) \hat { i } - 6 \hat { j } + 3 \hat { k }$ and $\vec { v } = \left( \log _ { e } b \right) \hat { i } + 2 \hat { j } + 2 a \left( \log _ { e } b \right) \hat { k } , ( b > 1 )$ is acute. Then $S$ is equal to\\
(1) $\left( - \infty , - \frac { 4 } { 3 } \right)$\\
(2) $\Phi$\\
(3) $\left( - \frac { 4 } { 3 } , 0 \right)$\\
(4) $\left( \frac { 12 } { 7 } , \infty \right)$

Paper Questions

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