In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the…
Mathematics20265 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)Statement 1 is true and Statement 2 is false.
(b)Statement 2 is true and Statement 1 is false.
(c)Both the statements are true.
(d)Both the statements are false.
(ii)[1.0]
A plane passes through three points A, B and C with position vectors $\hat{i} + \hat{j}$, $\hat{j} + \hat{k}$ and $\hat{k} + \hat{i}$ respectively. The equation of the line passing through the point P with position vector $\hat{i} + 2\hat{j} + 2\hat{k}$ and normal to the plane is (Application)
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)$c = \pm\sqrt{3}$
(d)$c > 2$
(iv)[1.0]
If $\vec{a}$ and $\vec{b}$ are unit vectors enclosing an angle $\theta$ and $|\vec{a}+\vec{b}| < 1$, then find the values between which $\theta$ lies. (Understanding)
(v)[1.0]
Shown below is a cuboid. Find $\vec{BA} \cdot \vec{BC}$ (Analysis)
