Question

IF line(OA) =4i + 3j, line(OB) = 6i - 2j and line(OC) =2i - j . Deduce the length of the triangle CA.

13−−√

20−−√

29−−√

17−−√
2 What quantity have both magnitude and direction ?
vector
scalar
mass
dot product
3 Find the vector product axb. If a = i + 2j - k and b = 2i + 3j + k
5i - 3j - k
2i - 4j - k
3i + j - k
I - j + 3k
4 A ...... is the sum of two vectors.
resultant vector
free vector
null vector
position vector
5 A temperature of
1000
C is a ...... quantity.
force
scalar
vector
magnitude

Answer 1

Answer on Question #52235 – Math – Vector Calculus

1. IF line(OA) = 4i + 3j, line(OB) = 6i - 2j and line(OC) = 2i - j. Deduce the length of the triangle CA.

13--v

20--v

29--v

17--v

2. What quantity have both magnitude and direction?

vector

scalar

mass

dot product

3. Find the vector product axb. If a = i + 2j - k and b = 2i + 3j + k

5i - 3j - k

2i - 4j - k

3i + j - k

1 - j + 3k

4. A ... is the sum of two vectors.

resultant vector

free vector

null vector

position vector

5 A temperature of

1000

C is a ... quantity.

force

scalar

vector

magnitude

Solution.

1.

$$\begin{array}{l} \overrightarrow {A C} = \overrightarrow {O C} - \overrightarrow {O A} = 2 i - j - (4 i + 3 j) = - 2 i - 4 j \\ \left| \overrightarrow {A C} \right| = \sqrt {(- 2) ^ {2} + (- 4) ^ {2}} = \sqrt {2 0} = 2 \sqrt {5} \approx 4. 4 7 \\ \end{array}$$

2. vector

3. The vector product (or the cross product) is

$$\begin{array}{l} a \times b = \left| \begin{array}{ccc} i & j & k \\ 1 & 2 & -1 \\ 2 & 3 & 1 \end{array} \right| = \left| \begin{array}{cc} 2 & -1 \\ 3 & 1 \end{array} \right| i - \left| \begin{array}{cc} 1 & -1 \\ 2 & 1 \end{array} \right| j + \left| \begin{array}{cc} 1 & 2 \\ 2 & 3 \end{array} \right| k = \\ = (2 * 1 - 3 * (-1)) i - (1 * 1 - 2 * (-1)) j + (1 * 3 - 2 * 2) k = \\ = 5 i - 3 j - k \end{array}$$

4. resultant vector

5. scalar

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