If the points whose position vectors are 2 hat i + hat j + hat k , 6 hat i - hat j +2 hat k and 14 hat i -5 hat j +p hat k are collinear, then the value of p is

Question

If the points whose position vectors are 2 hat i + hat j + hat k , 6 hat i - hat j +2 hat k and 14 hat i -5 hat j +p hat k are collinear, then the value of p is (A) 2 (B) 4 (C) 6 (D) 8

Tardigrade Admin · Accepted Answer

Given vectors vec a =2 hat i + hat j + hat k , vec b =6 hat i - hat j +2 hat k and vec c =14 hat i -5 hat j +p hat k are collinear, therefore [ vec a vec b vec c ]=0 ⇒ |2 1 1 6 -1 2 14 -5 p|=0 ⇒ 2[-p+10]-1[6 p-28]+1[-30+14]=0 ⇒ -2 p+20-6 p+28-16=0 ⇒ -8 p+ 32=0 ⇒ p=4

Q. If the points whose position vectors are 2i^+j^​+k^,6i^−j^​+2k^ and 14i^−5j^​+pk^ are collinear, then the value of p is

2

4

6

8

Given vectors a=2i^+j^​+k^,b=6i^−j^​+2k^ and c=14i^−5j^​+pk^ are collinear, therefore [abc]=0 ⇒∣∣​2614​1−1−5​12p​∣∣​=0 ⇒2[−p+10]−1[6p−28]+1[−30+14]=0 ⇒−2p+20−6p+28−16=0 ⇒−8p+32=0 ⇒p=4

Q. If the points whose position vectors are $2 \hat{i} + \hat{j} + \hat{k}, 6 \hat{i} - \hat{j} + 2 \hat{k}$ and $14 \hat{i} - 5 \hat{j} + p \hat{k}$ are collinear, then the value of $p$ is