What is the unit vector that is orthogonal to the plane containing # (8i + 12j + 14k) # and # (3i – 4j + 4k) #?

Answer 1

Use the cross product to find the vector # v_1 xx v_2_|_ = v_3#
#v_3 =104i +10j -68k #
#vec(u_3) = 1/sqrt(104^2+10^2+68^2)(104i +10j -68k) #

let # vec(v_1) = (8, 12, 14) and vec(v_2) = (3, -4, 4) # cross product #vec(v_1)xx vec(v_2) = [(12xx4) +(14xx4)] i + [(14xx3) -(8xx4)] j + [(8xx-4 - 12xx3)]k#

To obtain the orthogonal vector, simplify.

#vec(v_3) =104i +10j -68k # To calculate the unit vector find: #vec(u_3) = 1/|vec(v_3)| vec(v_3) # where: #|vec(v_3)| = magnitude# #|vec(v_3)| = sqrt(104^2+10^2+68^2)#
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Answer 2

To find the unit vector orthogonal to the plane containing the given vectors, first, find the cross product of the two vectors. Then, normalize the resulting vector to obtain the unit vector.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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