4.3. Figure shows the orientation of two vectors u and v in the XY plane.

$\text{ If }\mathrm{u}=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}\text{ and }\mathrm{v}=\mathrm{p}\hat{\mathrm{i}}+\mathrm{q}\hat{\mathrm{j}}$

which of the following is correct?

4.4. The component of a vector r along the X-axis will have maximum value if

4.6. Consider the quantities of pressure, power, energy, impulse gravitational potential, electric charge, temperature, area. Out of these, the only vector quantities are

Three vectors A, B, and C add up to zero. The incorrect statements are:
a. vector (A×B)×C is not zero unless vectors B, C are parallel.
b. vector (A×B).C is not zero unless vectors B, C are parallel.
c. if vectors A, B, C define a plane, (A×B)×C is in that plane.
d. (A×B).C = |A||B||C| $\to$ C² = A² + B²

4.10. It is found that |A + B| = |A|. This necessarily implies

4.15. For two vectors A and B, |A+B|=|A - B| is always true when:

a) |A| = |B| $\ne$ 0

b) $\mathrm{A} \perp \mathrm{B}$

c) |A| = |B| $\ne$ 0 and A and B are parallel or antiparallel.

d) when either |A| or |B| is zero.

4.1 The angle between $\mathrm{A}=\hat{\mathrm{i}}+\hat{\mathrm{j}} \mathrm{and} \mathrm{B}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ is

The magnitude of the resultant of two forces A = 8 N and B = 6 N acting at a point angle of $90°$ between them is:

The scalar and vector product of two vectors, $\overrightarrow{\mathrm{a}} = \left(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right)$ and $\overrightarrow{\mathrm{b}} = \left(-2\hat{\mathrm{i}}+\hat{\mathrm{j}}-3\hat{\mathrm{k}}\right)$ is equal to: