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:
A) $- 104 i + 72 j - 39 k$
B) $- 124 i + 62 j - 33 k$
C) $104 i - 91 j - 39 k$
D) $- 114 i - 12 j + 91 k$

Question

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: 
A) $- 104 i + 72 j - 39 k$
B) $- 124 i + 62 j - 33 k$
C) $104 i - 91 j - 39 k$
D) $- 114 i - 12 j + 91 k$

Quizplus · Accepted Answer

The vector product (or cross product) of two given vectors is given by:
$$V_1 \times V_2 = \begin{vmatrix} i & j & k \ 5 & 7 & -3 \ 7 & 2 & 14 \end{vmatrix}$$
Expanding the determinant, we get:
$$V_1 \times V_2 = (7 \times (-3) - 2 \times (-3))\textbf{i} - (14 \times 5 - 7 \times (-3))\textbf{j} + (5 \times 2 - 7 \times 7)\textbf{k} = \textbf{104i - 91j - 39k}$$
Therefore, the correct answer is option C.

Vector V1 is (5i+7j−3k) and V2=(7i+2j+14k)V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and } V _ { 2 } = ( 7 i + 2 j + 14 k )V1​ is (5i+7j−3k) and V2​=(7i+2j+14k)

Vector $V _ { 1 } \text { is } ( 5 i + 7 j - 3 k ) \text { and } V _ { 2 } = ( 7 i + 2 j + 14 k )$