MCQ
A vector which bisects the angle between $a =3 i -4 k$ and $b =5 j +12 k$ is
- A$39 i -25 j +8 k$
- ✓$39 i +25 j +8 k$
- C$3 i -5 j +\frac{8}{5} k$
- D$3 i +5 j +\frac{8}{5} k$
We have,
$a =3 i -4 k$ and $b =5 j +12 k$
We know that,
angle bisector of vector $a$ and $b$
$=\lambda\left[\frac{ a }{| a |}+\frac{ b }{| b |}\right]$
$\therefore \lambda\left[\frac{3 \hat{ i }-4 \hat{ k }}{5}+\frac{5 \hat{ j }+12 \hat{ k }}{13}\right]$
$=\lambda\left[\frac{39 \hat{ i }-52 \hat{ k }+25 \hat{ j }+60 \hat{ k }}{65}\right]$
$=\lambda[39 \hat{ i }+2 \hat{ j}+8 \hat{ k }]$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| List $I$ | List $II$ |
| $P.\quad$ Volume of parallelopiped determined by vectors $\vec{a}, \vec{b}$ and $\overrightarrow{ c }$ is $2$ . Then the volume of the parallelepiped determined by vectors $2(\vec{a} \times \vec{b}), 3(\vec{b} \times \vec{c})$ and $(\vec{c} \times \vec{a})$ is | $1.\quad$ $100$ |
| $Q.\quad$ Volume of parallelepiped determined by vectors $\vec{a}, \vec{b}$ and $\vec{c}$ is $5$ . Then the volume of the parallelepiped determined by vectors $3(\overrightarrow{ a }+\overrightarrow{ b }),(\overrightarrow{ b }+\overrightarrow{ c })$ and $2(\overrightarrow{ c }+\overrightarrow{ a })$ is | $2.\quad$ $30$ |
| $R.\quad$ Area of a triangle with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $20$ . Then the area of the triangle with adjacent sides determined by vectors $(2 \vec{a}+3 \vec{b})$ and $(\vec{a}-\vec{b})$ is | $3.\quad$ $24$ |
| $S.\quad$ Area of a paralelogram with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is $30$ . Then the area of the parallelogram with adjacent sides determined by vectors $(\vec{a}+\vec{b})$ and $\vec{a}$ is | $4.\quad$ $60$ |
Codes: $ \quad P \quad Q \quad R \quad S $