DAE MATH-113

Applied Mathematics-I

Chapter 8 : Vectors and Scalars

DAE Common Technologies | First Year

Multiple Choice Questions

Chapter:08 (Vectors and Scalars)

Question 1:

Magnitude of the vector $2i – 2j – k$ is:

4 3 2 1

Question 2:

Unit vector of $i + j + k$ is:

i + j + k

$i + j + k$

\frac{1}{3} (i + j + k)

${{\frac{1}{3}}(i + j + k)}$

\frac{1}{\sqrt{3}} (i + j + k)

${{\frac{1}{\sqrt{3}}}(i + j + k)}$

\frac{1}{2} (i + j + k)

${{\frac{1}{2}}(i + j + k)}$

Question 3:

Unit vector of $i – 2j – 2k$ is:

i - 2 j - 2 k

$i – 2j – 2k$

\frac{1}{3} (i - 2 j - 2 k)

${{\frac{1}{3}}(i – 2j – 2k)}$

\frac{1}{\sqrt{3}} (i - 2 j - 2 k)

${{\frac{1}{\sqrt{3}}}(i – 2j – 2k)}$

\frac{1}{2} (i - 2 j - 2 k)

${{\frac{1}{2}}(i – 2j – 2k)}$

Question 5:

The magnitude of a vector $\hat{i}-3\hat{j}+5\hat{k}$ is:

3

$3$

25

$25$

35

$35$

\sqrt{35}

$\sqrt{35}$

Question 7:

If θ is the angle between the vector ${\vec{a}}$ and ${\vec{b}}$ , then cos θ is:

\to a . \to b

${\vec{a}}.{\vec{b}}$

\frac{\to a . \to b}{| \to a | | \to b |}

${\frac{{\vec{a}}.{\vec{b}}}{|\vec{a}||\vec{b}|}}$

\frac{\to a . \to b}{| \to a |}

${\frac{{\vec{a}}.{\vec{b}}}{|\vec{a}|}}$

\frac{\to a . \to b}{| \to b |}

${\frac{{\vec{a}}.{\vec{b}}}{|\vec{b}|}}$

Question 8:

If $\vec{a}$ = ${a_1}i+{a_2}j+{a_3}k$ , $\vec{b}$ = ${b_1}i+{b_2}j+{b_3}k$ , then $\vec{a}.\vec{b}$ is:

a_{1} b_{1} j + a_{2} b_{2} j + a_{3} b_{3} k

${a_1}{b_1}j+{a_2}{b_2}j+{a_3}{b_3}k$

a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3}

${a_1}{b_1}+{a_2}{b_2}+{a_3}{b_3}$

a_{1} b_{2} j + a_{2} b_{3} j + a_{3} b_{1} k

${a_1}{b_2}j+{a_2}{b_3}j+{a_3}{b_1}k$

N o n e o f t h e s e

$None of these$

Question 9:

${\vec{a}}.{\vec{b}}=0$ implies that ${\vec{a}}$ and ${\vec{b}}$ are:

Perpendicular Parallel Non-parallel Oblique

Question 10:

If $\vec{a}$ = $i + j + k$ and $\vec{b}$ = $-i-j-mk$ are perndicular then m will be equal to:

1

$1$

2

$2$

\pm 1

${\pm}1$

\pm 3

${\pm}3$

Question 13:

If $\vec{a}$ = $2i-3j+k$ and $\vec{b}$ = $-i+2j+7k$ then $\vec{a}$ . $\vec{b}$ is equal to:

-1 -2 -3 -4

Question 14:

If $\vec{a}$ x $\vec{b}$ =0 then $\vec{a}$ and $\vec{b}$ is:

Non-parallel Parallel Perpendicular None of these

NOTE
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INSTRUCTOR
MUHAMMAD BIN JAMEEL
BSC ENGG. CIVIL

PBTE | DAE | MATH-113 APPLIED MATHEMATICS-I | MCQs | Chapter : 08 Vectors and Scalars