Exam 1: Introduction

$\text { Vector } V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text {, vector } V _ { 2 } \text { is } ( 7 i + 2 j + 14 k ) \text {, and vector } V _ { 3 } \text { is } ( i - 2 j + 5 k ) \text {. The scalar triple }$ product $\cdot \left( V _ { 2 } \times V _ { 3 } \right) \text { is }$

Vector $V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and } V _ { 2 } = ( 7 i + 2 j + 14 k )$ ). The scalar product of these two vectors is:

Force $F$ (see figure) is applied at C and is directed toward A. Its magnitude is $F = 15 \mathrm {~N} . \mathrm { A }$ unit vector along line CA is:

Vectors $V _ { 1 } \text { and } V _ { 2 }$ are orthogonal. If $\text { If } V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and } V _ { 2 } = \left( 7 i + V _ { y } j + 14 k \right)$ ), then component $V _ { y }$ in vector $V _ { 2 }$ is:

magnitudes of two vectors $V _ { a } \text { and } V _ { b } \text { are } 5 \text { and } 7 \text {, respectively, and the magnitude of their sum } V _ { s } \text { is }$ $10 \text { (i.e., } \left| V _ { a } \right| = 5 , \left| V _ { b } \right| = 7 , \left| V _ { s } \right| = 10 \text { ). The angles } \theta \text { and } \beta \text { in the figure below are: }$

$\text { The direction cosines of the vector } ( 4 \boldsymbol { i } - 8 \boldsymbol { j } + 7 \boldsymbol { k } ) \text { are: }$

$\text { Vector } V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and vector } V _ { 2 } \text { is } ( 7 i + 2 j + 14 k ) \text {. The component of } V _ { 1 } \text { parallel to the line of }$ action of vector $V _ { 2 }$ is:

Vector $V _ { 1 } \text { is } ( 5 \boldsymbol { i } + 7 \boldsymbol { j } - 3 \boldsymbol { k } ) \text { and vector } \boldsymbol { V } _ { 2 } \text { is } ( 7 \boldsymbol { i } + 2 \boldsymbol { j } + 14 \boldsymbol { k } )$ ). The component of $V _ { 1 }$ perpendicular to the line of action of vector $V _ { 2 }$ is:

sum of orthogonal vectors $V _ { 1 } \text { and } V _ { 2 } \text { is } ( 4 i - 8 j + 7 k )$ . A unit vector along $V _ { 1 }$ is $( 0.635 i + 0.773 j )$ Vector $V _ { 1 }$ is:

Vector $V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and } V _ { 2 } = ( 7 i + 2 j + 14 k )$ ). The vector product of these two vectors is: