Question

Evaluate: (3i-2j+k)•(7i+5j-12k)×(5i-13j+19k)​

Answer 1

Answer:

491

Step-by-step explanation:

To find the triple product of three vectors, always do the cross product first. If you do the dot product first you end up with a scalar and you can't cross a scalar and a vector.

so (7, 5, -12) x (5, -13, 19) can be found using the matrix determinant method

| i    j  k |

|7,  5, 12| = i(5*19 - 12*(-13)) - j(7*19 - 5*12) + k(-13*7 - 5*5) = (251, 73, -116)

|5, -13, 19|

then we can dot that result with the first vector to get the answer

(3, -2, 1) . (251, 73, -116) = 3 * 251 -2 * 73 - 116 * 1 =  491

Answer 2

Answer:

To find the triple product of three vectors, always do the cross product first. If you do the dot product first you end up with a scalar and you can't cross a scalar and a vector.

so (7, 5, -12) x (5, -13, 19) can be found using the matrix determinant method

| i    j  k |

|7,  5, 12| = i(5*19 - 12*(-13)) - j(7*19 - 5*12) + k(-13*7 - 5*5) = (251, 73, -116)

|5, -13, 19|

then we can dot that result with the first vector to get the answer

(3, -2, 1) . (251, 73, -116) = 3 * 251 -2 * 73 - 116 * 1 =  491

Step-by-step explanation: