Definition of Vector

Q. The magnitude of the position vector of the point (3, 4) will be ___

Q.

A, B, C and D form the coordinates of a trapezium.What would be the perimeter of the trapezium?

1. 11 + √13 units

2. 13 + √11 units

3. 13 units

4. 11 units

Q.

Triangle ADC is formed by joining the coordinates A(2, 6), C(4, 0) and D(0, 0). Another $\Delta$ BCD is formed by joining the coordinates B(6, 6), C(4, 0) and D(0, 0). Line y=6 and y=0 is parallel to each other. The points C(4, 0) and D(0, 0) lies on y = 0. The points A(2, 6) and B(6, 6) lies on line y=6. ABCD forms a quadrilateral. Which of the following is correct?

1. Quadrilateral ABCD is square.

2. Quadrilateral ABCD is rectangle.

3. Quadrilateral ABCD is parallelogram.

4. Quadrilateral ABCD is rhombus.

Q. Question 12
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4) then
(A) $AP=\frac{1}{3}AB$
(B) $AP=PB$
(C) $PB=\frac{1}{3}AB$
(D) $AP=\frac{1}{2}AB$

Q. A vector $\overrightarrow{a}$ has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system. $\overrightarrow{a}$ has components p + 1 and 1, then

1. p = 0
2. $p=1orp=-\frac{1}{3}$
3. $p=1orp=-1$
4. $p=-1orp=\frac{1}{3}$

Q. Consider points A, B, C and D with position vectors$<6,-4,7>,<1,-6,10>,<-1,-3,4>and<5,-1,5>$ respectively. Then ABCD is a

1. square
2. rhombus
3. rectangle
4. none of these