Question

Determine whether the given vectors are orthogonal, parallel, or neither. (a) a = <9, 3>, b = <-2, 6> orthogonal parallel neither (b) a = <4, 7, -2>, b = <3, -1, 7> orthogonal parallel neither (c) a = -12i + 4j + 8k, b = 9i - 3j - 6k orthogonal parallel neither (d) a = 3i - j + 3k, b = 3i + 3j - 2k orthogonal parallel neither

          Determine whether the given vectors are orthogonal, parallel, or neither.
(a) a = <9, 3>, b = <-2, 6>
orthogonal
parallel
neither
(b) a = <4, 7, -2>, b = <3, -1, 7>
orthogonal
parallel
neither
(c) a = -12i + 4j + 8k, b = 9i - 3j - 6k
orthogonal
parallel
neither
(d) a = 3i - j + 3k, b = 3i + 3j - 2k
orthogonal
parallel
neither

Determine whether the given vectors are orthogonal, parallel, or neither.
(a) a = <9, 3>, b = <-2, 6>
orthogonal
parallel
neither
(b) a = <4, 7, -2>, b = <3, -1, 7>
orthogonal
parallel
neither
(c) a = -12i + 4j + 8k, b = 9i - 3j - 6k
orthogonal
parallel
neither
(d) a = 3i - j + 3k, b = 3i + 3j - 2k
orthogonal
parallel
neither

Added by Morgan H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

Step 1

For a = (9, 3) and b = (-2, 6), we can check if they are orthogonal by taking their dot product: a · b = (9)(-2) + (3)(6) = -18 + 18 = 0 Since the dot product is 0, the vectors are orthogonal. So, the answer for the first pair is $\boxed{\text{orthogonal}}$. Show more…

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Determine whether the given vectors are orthogonal, parallel, or neither. (a) a = (9, 3), b = (-2, 6) orthogonal parallel neither (b) a = (4, 7, -2), b = (3, -1, 7) orthogonal parallel neither (c) a = -12i + 4j + 8k, b = 9i - 3j - 6k orthogonal parallel neither (d) a = 3i - j + 3k, b = 3i + 3j - 2k orthogonal parallel neither