‹ Back to the paper
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the…
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
(i)[1.0]
If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j}$, find $t$ such that $\vec{a} + t\vec{b}$ is perpendicular to $\vec{c}$ is
- (a)$0$
- (b)$5$
- (c)$4$
- (d)$2$
(ii)[1.0]
The planes $2x - y + 4z = 5$ and $5x - 2\cdot 5y + 10z = 6$ are
- (a)parallel
- (b)intersect on y axis
- (c)perpendicular
- (d)pass through $(0, 0, \frac{5}{4})$
(iii)[1.0]
Find a vector of magnitude of $10$ units and parallel to the vector $2\hat{i} + 3\hat{j} - \hat{k}$.
(iv)[1.0]
Find the position vector of a point R which divides the line joining the two-points $P$ and $Q$ with position vectors $2\hat{i} + \hat{j}$ and $\hat{i} - 2\hat{j}$ respectively in the ratio of $2:1$ externally.
(v)[1.0]
Find the equation of the plane with intercept $3$ on the $y\text{--axis}$ and parallel to $xz\text{--plane}$.
Answer
No answer yet.
From ISC 2023 Specimen Mathematics Paper 1, question 15.