Question

Consider the points P(2,3,5) and Q(5,2,3) 1(a) Let a be the vector from P towards Q. Find a algebraically, and express in component form: 1(b) Express vector a in " ijk " form: 1(c) Express the vector −a in " ijk " form:

Answer 1

Vector a from P to Q is given by the differences in their coordinates resulting in (3, -1, -2). In ijk form, it's expressed as 3i - j - 2k. The negation of vector a, or -a, in ijk form is -3i + j + 2k.

Step-by-step explanation:

To find the vector a from point P(2,3,5) towards Q(5,2,3), we subtract the coordinates of P from the coordinates of Q:

• Vector a = (Qx - Px, Qy - Py, Qz - Pz)
• Vector a = (5 - 2, 2 - 3, 3 - 5)
• Vector a = (3, -1, -2)

In ijk form, this can be expressed as:

• Vector a = 3i - j - 2k

To express the vector -a, simply negate each component of vector a:

• Vector -a = -3i + j + 2k