In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the…
Mathematics20245 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]
If $\vec{a} = 3\hat{i} - 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} - 4\hat{j} - 3\hat{k}$ then the value of $|\vec{a} - 2\vec{b}|$ will be:
(a)$\sqrt{85}$
(b)$\sqrt{86}$
(c)$\sqrt{87}$
(d)$\sqrt{88}$
(ii)[1.0]
If a line makes an angle $\alpha$, $\beta$ and $\gamma$ with positive direction of the coordinate axes, then the value of $\sin^2\alpha + \sin^2\beta + \sin^2\gamma$ will be:
(a)1
(b)3
(c)-2
(d)2
(iii)[1.0]
In the figure given below, if the coordinates of the point $P$ are $(a, b, c)$, then what are the perpendicular distances of $P$ from $XY$, $YZ$ and $ZX$ planes respectively?
(iv)[1.0]
If $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b} = 5\hat{i} - 3\hat{j} + \hat{k}$, find the projection of $\vec{b}$ on $\vec{a}$.
(v)[1.0]
Find a vector of magnitude 20 units parallel to the vector $2\hat{i} + 5\hat{j} + 4\hat{k}$.
