Question

Vector Vector C D. has an initial point of (–7, 2, 8) and a terminal point of (0, 7, 3). Vector Vector E F. has an initial point of (4, 1, –2) and a terminal point of (6, –2, –3). What is the component form of vector Vector C D minus vector E F.?

LeftAngleBracket negative 5, negative 8, 4 RightAngleBracket.
LeftAngleBracket 5, 8, negative 4 RightAngleBracket.
LeftAngleBracket 9, 2, negative 6 RightAngleBracket.
LeftAngleBracket negative 9, negative 2, 6 RightAngleBracket.

Answer 1

A vector is a quantity in physics that has both magnitude and direction. The component form of Vector CD minus vector EF is <5, 8, -4>.

What is a vector?

A vector is a quantity in physics that has both magnitude and direction. It is often represented by an arrow whose length is proportionate to the magnitude of the quantity and whose direction is the same as that of the quantity.

The value of the Vector CD can be written as,

$|\vec{CD}| = (0+7)\hat i+(7-2)\hat j+(3-8)\hat k = 7\hat i+5\hat j-5\hat k$

The value of the Vector EF can be written as,

$|\vec{EF}| = (6-4)\hat i+(-2-(-1))\hat j+(-3-(-2))\hat k = 2\hat i-3\hat j-5\hat k$

Now,  the component form of Vector CD minus vector EF can be written as,

$\vec{CD} - \vec{EF} = < (7-2) , (5-(-3)) , (-5-(-1)) > = < 5,8,-4 >$

Hence, the component form of Vector CD minus vector EF is <5, 8, -4>.

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