Find a + b, 2a + 3b, |a|, and |a - b|. a = i + 4j - 3k, b = -4i - j + 5k

Solution:

Given vectors are

a = i + 4j - 3k, b = -4i - j + 5k

a + b = ( i + 4j - 3k) + ( -4i - j + 5k)

a + b= (1 - 4)i + (4 - 1)j + (5 - 3)k

a + b= -3i + 3j + 2k ---------> [a]

2a = 2(i + 4j - 3k) = 2i + 8j - 6k

3b = 3( -4i - j + 5k) = -12i - 3j + 15k

2a + 3b = (2i + 8j - 6k) + (-12i - 3j + 15k )

2a + 3b = -10i + 5j + 11k ---------> [b]

|a| = √1² + 4² + (-3)² = √1 + 16 + 9 = √26 ---------> [c]

a - b = ( i + 4j - 3k) - ( -4i - j + 5k)

a - b = (1 - (-4))i + (4 + 1)j + (-3 - 5)k

a - b = (1 + 4)i + (4 + 1)j - (3 + 5)k

a - b = 5i +5j -8k ---------> [d]

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Find a + b, 2a + 3b, |a|, and |a - b|. a = i + 4j - 3k, b = -4i - j + 5k

Summary:

The values of a + b, 2a + 3b, |a|, and |a - b|. a = i + 4j - 3k, b = -4i - j + 5k are -3i + 3j + 2k , -10i + 5j + 11k , √26, 5i + 5j - 8k respectively.