In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the…
Mathematics20255 marksShort answer
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
(i)[1.0]
Consider the following statements and choose the correct option:
Statement 1: If $\vec{a}$ and $\vec{b}$ represents two adjacent sides of a parallelogram then the diagonals are represented by $\vec{a} + \vec{b}$ and $\vec{a} - \vec{b}$.
Statement 2: If $\vec{a}$ and $\vec{b}$ represents two diagonals of a parallelogram then the adjacent sides are represented by $2(\vec{a} + \vec{b})$ and $2(\vec{a} - \vec{b})$.
Which of the following is correct? [Recall]
(a)Only Statement 1
(b)Only Statement 2
(c)Both Statements 1 and 2
(d)Neither Statement 1 nor Statement 2
(ii)[1.0]
The distance of the plane through $(1, 1, 1)$ and perpendicular to the line $\frac{x-1}{3} = \frac{y-1}{0} = \frac{z-1}{4}$ from the origin is [Application]
(a)$\frac{3}{4}$
(b)$\frac{4}{3}$
(c)$\frac{7}{5}$
(d)1
(iii)[1.0]
If the direction cosines of a line are $\left\langle \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \right\rangle$ then [Understanding]
(a)c > 0
(b)0 < c < 1
(c)c = ±3
(d)c > 2
(iv)[1.0]
If $\vec{a}$ is a unit vector perpendicular to $\vec{b}$ and $(\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) = -5$, find $|\vec{b}|$. [Understanding]
(v)[1.0]
Shown below is a cuboid. Find $\vec{BA} \cdot \vec{BC}$. [Analysis]
