AP EAPCET 2024 - 19th May Evening Shift | Vector Algebra Question 30 | Mathematics

Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ and $\mathbf{v}=\mathbf{a} \times \mathbf{b}$, then $|\mathbf{v}|=$

$|\mathbf{u}|+|\mathbf{u} \cdot \mathbf{v}|$

$\frac{|\mathbf{u}|}{2}$

$|\mathbf{u}|+\frac{|\mathbf{u} \cdot \mathbf{b}|}{2}$

$\frac{|\mathbf{u}|}{5}$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

In a regular hexagon $A B C D E F, \mathbf{A B}=\mathbf{a}$ and $\mathbf{B C}=\mathbf{b}$, then $F A=$

$\mathbf{a}-\mathbf{b}$

$a+b$

$\mathbf{b}-\mathbf{a}$

$2 \mathbf{b}-\mathbf{a}$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\mathbf{f}, \mathbf{g}, \mathbf{h}$ be mutually orthogonal vectors of equal magnitudes, then the angle between the vectors $\mathbf{f}+\mathbf{g}+\mathbf{h}$ and $\mathbf{h}$ is

$\cos ^{-1}\left(\frac{\sqrt{3}}{4}\right)$

$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\pi-\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$

$\pi-\cos ^{-1}\left(\frac{\sqrt{3}}{4}\right)$

AP EAPCET 2024 - 18th May Morning Shift

MCQ (Single Correct Answer)

-0

Let $\mathbf{a}, \mathbf{b}$ be two unit vectors. If $\mathbf{c}=\mathbf{a}+2 \mathbf{b}$ and $\mathbf{d}=5 \mathbf{a}-4 \mathbf{b}$ are perpendicular to each other, then the angle between $a$ and $b$ is

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{8}$

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