AP EAPCET 2024 - 22th May Morning Shift | Vector Algebra Question 12 | Mathematics

If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ and $\sin \theta=\sqrt{\frac{24}{28}}$, then $7 a^2+24 a=$

AP EAPCET 2024 - 21th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}},-3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of three points, $A, B, C$ respectively, then $A, B, C$

are collinear point

form an isosceles triangle which is not equilateral

form an equilateral trianglé

form a scalene triangle

AP EAPCET 2024 - 21th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ are position vectors of 4 points such that $2 a+3 b+5 c-10 d=0$, then the ratio in which the line joining $c$ and $d$ divides the line segment joining $a$ and $\mathbf{b}$ is

$2: 3$

$-1: 2$

$2: 1$

$3: 2$

AP EAPCET 2024 - 21th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are 3 vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=8,|\mathbf{c}|=11$ and $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$, then the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is

$\cos ^{-1} \frac{2}{5}$

$\cos ^{-1} \frac{10}{11}$

$\cos ^{-1} \frac{41}{55}$

$\frac{\pi}{3}$

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