441.

If the vector 8i + aj of magnitude 10 is in the direction of the vector 4i + 3j, then the value of equal to

• 6

• 3

• - 3

• - 6

If a = 2i - 7j + k and b = i + 3j - 5k and a · mb = 120, then the value of m is equal to

• 5

• - 24

• - 5

• 120

The position vector of the centroid of the $∆$ABC is 2i + 4 j + 2k. If the position vector of the vertex A is 2i + 6j + 4k, then the position vector of midpoint of BC is

• 2i + 3j + k

• 2i + 3j - k

• 2i - 3j - k

• - 2i - 3j - k

If the vectors 3i - 4j - k and 2i + 3j - 6k represent the diagonals of a rhombus, then the length of the side of the rhombus is

• 15

• $15\sqrt{3}$

• $\frac{5\sqrt{3}}{2}$

• $\frac{15\sqrt{3}}{2}$

If a = 2i + 3j + $\mathrm{\alpha }$k and b = 3i - $\mathrm{\alpha }$j + 2k, then the angle between a + b and a-b is equal to

• 0

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

If a = 2i + 2j - k, b = $\mathrm{\alpha i} + \mathrm{\beta j}$ + 2k and $\left|\mathrm{a} + \mathrm{b}\right| = \left|\mathrm{a} - \mathrm{b}\right|$, then $\mathrm{\alpha } + \mathrm{\beta }$ is equal to

• 2

• 1

• 0

• - 1

If the projection of b on a is twice the projection of a on b, then $\left|\mathrm{b}\right| - \left|\mathrm{a}\right|$ is equal to 

• $\left|\mathrm{a} - \mathrm{b}\right|$

• $\left|\mathrm{a}\right| + \left|\mathrm{b}\right|$

• $\left|\mathrm{b}\right|$

• $\left|\mathrm{a}\right|$

If a = i - j and b = j + k, then then ${\left|\mathrm{a} \times \mathrm{b}\right|}^2 + {\left|\mathrm{a} . \mathrm{b}\right|}^2$ is equal to

• $\sqrt{2}$

• 2

• $\sqrt{6}$

• 4

If $\left|\mathrm{a}\right| = 1, \left|\mathrm{b}\right| = 3 \mathrm{and} \left|\mathrm{a} - \mathrm{b}\right| = \sqrt{7}$, then the angle between a and b is

• 0

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

A vector of magnitude 7 units, parallel to the resultant of the vectors a = 2 i - 3j - 2k and b = - i + 2j + k, is

• $\frac{7}{\sqrt{3}}\left(\mathrm{i} +\hspace{0.17em}\mathrm{j}\hspace{0.17em}+\hspace{0.17em}\mathrm{k}\right)$

• 7(i - j - k)

• $\frac{7}{\sqrt{3}}\left(\mathrm{i} - \mathrm{j} +\hspace{0.17em}\mathrm{k}\right)$

• $\frac{7}{\sqrt{3}}\left(\mathrm{i} - \mathrm{j} - \mathrm{k}\right)$