If a vector 2i+3j+8k is perpendicular to the vector 4i-4j+ak,then the value of a is

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Transcript

00:00the question is if a vector 2i plus 3j plus 8k is perpendicular to the vector

00:144i minus 4j plus alpha k then the value of alpha is a minus 1 b 1 upon 2 c minus

00:261 upon 2 b 1 take a suppose 2i plus 3j plus 8k is a vector and 4i minus 4j plus

00:37alpha k is b vector so a vector is perpendicular to the b vector so when a

00:47vector is perpendicular to the b vector then their dot product will be 0 so a

00:54dot B is equal to 0 as the value of a is 2i plus 3j plus 8k dots the value of B

01:20is 4i minus 4j plus alpha k is equal to 0 for simplification we will multiply

01:41the value of I with I the value of J with J and the value of K with K so 2i

01:55into 4i it will be 8 I dot I plus into minus it will be minus 3 into 4 it will

02:08be 12 J dot J plus into plus it will be plus 8 into alpha it will be 8 alpha K

02:19dot K is equal to 0 as we have studied that the value of I dot I is equal to J

02:29dot J is equal to K dot K is equal to 1 so 8 into 1 it will be 8 minus 12 plus

02:438 alpha is equal to 0 so plus 8 minus 12 so it will be minus 4 plus 8 into alpha

02:58is equal to 0 so we have to find the value of alpha so 8 alpha is equal to

03:05when we will take minus 4 on the other side of equal then it will be plus 4 so

03:14alpha will be obtained as 4 here 8 is multiplying with alpha on the other side

03:22of equal it will divide with 4 so the table of 4 on 4 is 1 times and on 8 is 2

03:31times is the value of alpha is obtained is 1 upon 2 so the correct option will be

03:40b 1 upon 2