Question

Let →a=ˆi+4ˆj+2ˆk,→b=3ˆi−2ˆj+7ˆkand→c=2ˆi−ˆj+4ˆk. Find a vector →d which is perpendicular to both →a and →b and →c.→d=15

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Answer 1

To find a vector that is perpendicular to both →a and →b and →c, we can take the cross product of any two of these vectors. Let's take the cross product of →a and →b: →d = →a x →b.

Step-by-step explanation:

To find a vector that is perpendicular to both →a and →b and →c, we can take the cross product of any two of these vectors. Let's take the cross product of →a and →b:

→d = →a x →b

Using the formula for the cross product of two vectors, we can calculate:

→d = (1)(7)→i - (3)(2)→j + (4)(-2)→k

→d = 7→i - 6→j - 8→k

Therefore, the vector →d that is perpendicular to both →a and →b is given by →d = 7→i - 6→j - 8→k.