Given that $a = i + j + k; b = i - j + k; c = i + j - k$ evaluate $(a + 2 b) . [a + (a . c) b]$

12

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5

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10

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4

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Solution

The correct option is D $12$
$(a + 2 b) . [a + (a . c) b] . = (i + j + k + 2 i - 2 j + 2 k) (i + j + k + (1 + 1 - 1) (i - j + k)) = (3 i - j + 3 k) (i + j + k + i - J + k) = (3 i - j + 3 k) (2 i + 2 k) = 6 + 0 + 6 = 12$

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Given that a=i+j+k;b=i−j+k;c=i+j−k evaluate (a+2b).[a+(a.c)b]

The correct option is D 12(a+2b).[a+(a.c)b].=(i+j+k+2i−2j+2k)(i+j+k+(1+1−1)(i−j+k))=(3i−j+3k)(i+j+k+i−J+k)=(3i−j+3k)(2i+2k)=6+0+6=12

Given that $a = i + j + k; b = i - j + k; c = i + j - k$ evaluate $(a + 2 b) . [a + (a . c) b]$

The correct option is D $12$
$(a + 2 b) . [a + (a . c) b] . = (i + j + k + 2 i - 2 j + 2 k) (i + j + k + (1 + 1 - 1) (i - j + k)) = (3 i - j + 3 k) (i + j + k + i - J + k) = (3 i - j + 3 k) (2 i + 2 k) = 6 + 0 + 6 = 12$