AP EAPCET 2024 - 21th May Evening Shift | Vector Algebra Question 14 | Mathematics

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

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

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

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

$\frac{\pi}{3}$

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

$\mathbf{a}=\alpha \hat{\mathbf{i}}+\beta \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \quad \mathbf{b}=\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ ar linearly dependent vectors and magnitude of $ \alpha $$ \sqrt{14} $${\text {}}{ }^{}$ If $\alpha, \beta$ are integers, then $\alpha+\beta=$

-3

-5

AP EAPCET 2024 - 21th May Morning Shift

MCQ (Single Correct Answer)

-0

$\mathbf{c}$ is a vector along the bisector of the internal angle between the vectors $\mathbf{a}=4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{b}=12 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$. If the magnitude of $\mathbf{c}$ is $3 \sqrt{13}$, then c=

$5 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+2 \sqrt{2 \hat{k}}$

$10 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{k}}$

$\mathbf{i}-10 \mathbf{j}+4 \mathbf{k}$

$2 \sqrt{2} \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\mathbf{8} \hat{\mathbf{k}}$

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