Question

Write the component form of the linear combination of the standard vector y = -35j + 12k.

a) <0, -35, 12>
b) <-35, 12, 0>
c) <12, -35, 0>
d) <0, 12, -35>

Answer 1

The component form of the vector y = -35j + 12k is in the format of an ordered triple and is represented as <0, -35, 12>, corresponding to option (a).

Step-by-step explanation:

The component form of the linear combination of the standard vector y = -35j + 12k is represented by writing the coefficients of the unit vectors i (for the x-component), j (for the y-component), and k (for the z-component) in the form of an ordered triple.

Since the vector given does not have an i component, its value is zero. Therefore, the i (x-component) is '0'. The coefficient of j is '-35', representing the y-component, and the coefficient of k is '12', representing the z-component. Thus, the component form is <0, -35, 12>, which matches option (a).