Addition of Vectors

Q. This is an Assertion(A) - Reason(R) type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

A: In the ΔABC , AB = 24 cm , BC = 10 cm and AC = 26 cm , then ΔABC is a right angle triangle.

R: If in two triangles, their corresponding angles are equal, then the triangles are similar.

1. Both A and R are true and R is not the correct explanation of A
2. Both A and R are true and R is the correct explanation of A
3. A is true but R is false
4. A is false and R is True

Q. Two forces of 3N and 4N are acting on a particle. The forces are acting at an angle of ${30}^{\circ }$ between them. The magnitude of the resultant force will be

1. $\sqrt{3^2+4^2}N$
2. $\sqrt{3^2+4^2+3\times 4cos30}N$
3. $\sqrt{3^2+4^2+3\times 4\times sin30}N$
4. $\sqrt{3^2+4^2+2\times 3\times 4cos30}N$

Q. AB, BC, CD, DE and EF are 5 vectors as shown in the figure.

Joining which 2 points will give the magnitude of resultant of $\overline{AB}+\overline{BC}+\overline{CD}+\overline{DE}+\overline{EF}$

1. A & E
2. A & D
3. A & F
4. A & C

Q. The angle between the diagonals of the parallelogram formed by the points $(1,2,3),(-1,-2,-1),(2,3,2),(4,7,6)$ is

1. $co{s}^{-1}\left(7\right)$
2. $co{s}^{-1}(\frac{7}{\sqrt{155}})$
3. $co{s}^{-1}(\frac{7}{\sqrt{465}})$
4. $co{s}^{-1}(\frac{7}{465})$

Q. $\mathrm{If}\mathrm{two}\mathrm{vectors}\overrightarrow{A}\mathrm{and}\overrightarrow{B}\mathrm{are}\mathrm{such}\mathrm{that}\left(\overrightarrow{A}+\overrightarrow{B}\right|>\left(\overrightarrow{A}-\overrightarrow{B}\right|\mathrm{then}\mathrm{the}\mathrm{angle}\mathrm{between}\overrightarrow{A}\mathrm{and}\overrightarrow{B}\mathrm{is}$

1. ${90}^o$
2. Less than ${90}^o$
3. More than ${90}^o$

Q. If $A(-2,1),B(a,b),C(4,6)$ and $D(1,2)$ are the vertices of parallelogram. Find $a+b$