The area of a parallelogram with $3\hat{\mathrm{i}} + \hat{\mathrm{j}} - 2\hat{\mathrm{k}} \mathrm{and} \hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 4\hat{\mathrm{k}}$ as diagonal is :

• $\sqrt{72}$

• $\sqrt{73}$

• $\sqrt{74}$

• $\sqrt{75}$

In a $∆\mathrm{ABC}$, if $\left(\sqrt{3} - 1\right)$a = 2b, A = 3B, then C is

• $60°$

• 120$°$

• 30°

• 45°

The x - axis, y - axis and a line passing through the point A (6, 0) from a $∆$ ABC. If $\angle$A = 30°, then the area of the $∆$, in sq unit is

• $6\sqrt{3}$

• $12\sqrt{3}$

• $4\sqrt{3}$

• 8$\sqrt{3}$

The mid point of the line joining the points (- 10, 8) and (- 6, 12)divides the line joining the points ( 4, - 2) and (- 2, 4) in the ratio

• 1 : 2 internally

• 1 : 2 externally

• 2 : 1 internally

• 2 : 1 externally

If from a point P (a, b, c) perpendiculars PA, PB are drawn to yz and zx planes, then the equation of the plane OAB is

• bcx + cay + abz = 0

• bcx + cay - abz = 0

• bcx - cay + abz = 0

• - bcx + cay + abz = 0

If P (x, y, z) is a point on the line segment joning Q (2, 2, 4) and R (3, 5, 6) such thatprojections of OP on the axes are $\frac{13}{5}, \frac{19}{5}, \frac{26}{5}$ respectively, then P divides QR in the ratio

• 1 : 2

• 3 : 2

• 2 : 3

• 1 : 3

The equation to the plane through the points (2, 3, 1) and ( 4, - 5 3) paralled to x - axis is

• x + y + 4z = 7

• x + 4z = 7

• y - 4z = 7

• y + 4z = 7

428.

The angle between r = (1 + 2µ)i +(2 + µ)j + (2µ - 1)k and the plane 3x - 2y + 6z = 0 (whereµ is a scalar) is

• ${\sin }^{-1}\left(\frac{15}{21}\right)$

• ${\cos }^{-1}\left(\frac{16}{21}\right)$

• ${\sin }^{-1}\left(\frac{16}{21}\right)$

• $\frac{\mathrm{\pi }}{2}$

The length of the shortest distance between the two lines r = (- 3i + 6j) + s (- 4i + 3j + 2k) and r = (- 2i + 7k) + t(- 4i + j + k) is

• 7 unit

• 13 unit

• 8 unit

• 9 unit

The perpendicular distance of the point (6, 5, 8) from y-axis is

• 5 unit

• 6 unit

• 8 unit

• 10 unit