Tag: directed angles

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Questions Related to directed angles

Multiple choice mathematics and statistics angle and its measurement directed angles

If $P,Q,R$ and $S$ are $(1,2,5),(-2,1,3),(4,4,2)$ and $(2,1,-4)$, then projection of $PQ$ on $RS$ be

  1. $2$
  2. $3$
  3. $4$
  4. $5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The vector PQ is calculated by subtracting coordinates of P from Q, and RS is found similarly. The projection of vector PQ on vector RS is given by the dot product of PQ and a unit vector in the direction of RS, resulting in 3.

Multiple choice mathematics and statistics angle and its measurement directed angles

The measure of co-terminal angle differ by an integral multiple of_________

  1. $90^{o}$
  2. $180^{o}$
  3. $360^{o}$
  4. $270^{o}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Co-terminal angles share the same initial and terminal sides, meaning they differ by a full rotation, which is 360 degrees or 2 pi radians.

Multiple choice mathematics and statistics angle and its measurement directed angles

The ratio between the complementary and the supplementary angles of an angle is $1:7$. What is the measure of that angle?

  1. $15^o$
  2. $75^o$
  3. $60^o$
  4. $65^o$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the angle be x. Its complementary angle is (90 - x) and its supplementary angle is (180 - x). Setting up the ratio (90 - x) / (180 - x) = 1/7 and solving gives x = 75 degrees.

Multiple choice mathematics and statistics angle and its measurement directed angles

The equation to the perpendicular bisector of the line segment joining (5,7) (3,1) is 

  1. $3x+y =16$
  2. $x - 3y =12$
  3. $x+ 3y =16$
  4. $3x - y =12$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here, $A=(5,7)$ and $B=(3,1)$


Here, $x _1=5,y _1=7,x _2=3$ and $y _2=1$


$\Rightarrow$  Mid-point of $A$ and $B=$ $\left(\dfrac{x _1+x _2}{2},\dfrac{y _1+y _2}{2}\right)$

                                            $=\left(\dfrac{5+3}{2},\dfrac{7+1}{2}\right)$

                                            $=\left(4,4\right)$

$\Rightarrow$  Slope of $AB\,(m)=\dfrac{1-7}{3-5}=\dfrac{-6}{-2}=3$

$\Rightarrow$  Slope of the perpendicular $(m _1)$ $=\dfrac{-1}{m}=\dfrac{-1}{3}$

The perpendicular passes through $(4,4)$.

The equation is,
$\Rightarrow$  $y-4=\dfrac{-1}{3}(x-4)$

$\Rightarrow$  $3y-12=-x+4$

$\Rightarrow$  $x+3y=16$

Multiple choice mathematics and statistics angle and its measurement directed angles

Mark the correct alternative of the following.
An angle of measure $360^o$ is called?

  1. A zero angle

  2. A straight angle

  3. A reflex angle

  4. A complete angle
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An angle of measure $360^o$ is called a complete angle. [ Using definition of complete angle]

Multiple choice mathematics and statistics angle and its measurement directed angles

 Angles of a triangle are in the ratio $3 : 4 : 5$. The smallest angle is $45^o$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Angles of the triangle are in the ratio $3 : 4: 5$
Let the angles be $3x, 4x$ and $5x$
Sum of the angles of the triangle $= 180$
Thus, $3x + 4x + 5x = 180$
$12x = 180$
$x = 15$
Thus, the angles are $45^{o}, 60^{o}$ and $75^{o}$.