AP EAPCET 2024 - 22th May Evening Shift | Vector Algebra Question 7 | Mathematics

Let $|\hat{\mathbf{a}}|=2=|\hat{\mathbf{b}}|=3$ and the angle between $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ be $\frac{\pi}{3}$. If a parallelogram is constructed with adjacent sides $2 \hat{\mathbf{a}}+3 \hat{\mathbf{b}}$ and $\hat{\mathbf{a}}-\hat{\mathbf{b}}$, then its shorter diagonal is of length

108

172

$6 \sqrt{3}$

$2 \sqrt{43}$

AP EAPCET 2024 - 22th May Evening Shift

MCQ (Single Correct Answer)

-0

The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}$ is obtuse lie in the interval

$(-\infty, 0) \cup(3, \infty)$

$(0,3)$

$[0,3]$

$(-\infty, 0) \cup 3, \infty)$

AP EAPCET 2024 - 22th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $\hat{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. The projection d the sum of the vectors $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ on the vector perpendicular to the plance of $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$, is

$4 \sqrt{2}$

$7 \sqrt{2}$

$\frac{1}{\sqrt{2}}$

AP EAPCET 2024 - 22th May Morning Shift

MCQ (Single Correct Answer)

-0

In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ and $(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \mathbf{k})$are$\mathbf{}$ the position vectors of the vectices $P, Q$ and $R$ respectively then, the position vector fo the point ol intersection of the angle bisector of $P$ and $Q R$ is

$(6 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$

$(2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}})$

$(5 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$

$\left(\frac{5}{2} \hat{\mathbf{i}}+\frac{3}{2} \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\right)$

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