CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

The value of the determinant is
∣ ∣ ∣cos(AP)cos(AQ)cos(AR)cos(BP)cos(BQ)cos(BR)cos(CP)cos(CQ)cos(CR)∣ ∣ ∣

A
zero for all values of P, Q, R, A, B, and C.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
one for all values of P, Q, R, A, B, and C.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
zero only if P= Q= R= A= B= C.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
one only if P= Q= R= A= B= C.
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A zero for all values of P, Q, R, A, B, and C.
Let Δ=∣ ∣ ∣cos(AP)cos(AQ)cos(AR)cos(BP)cos(BQ)cos(BR)cos(CP)cos(CQ)cos(CR)∣ ∣ ∣
Δ=∣ ∣ ∣cos A cos P+sin A sin Pcos(AQ)cos(AR)cos B cos P+sin B sin Pcos(BQ)cos(BR)cos C cos P+sin C sin Pcos(CQ)cos(CR)∣ ∣ ∣
Δ=∣ ∣ ∣cos A cos Pcos(AQ)cos(AR)cos B cos Pcos(BQ)cos(BR)cos C cos Pcos(CQ)cos(CR)∣ ∣ ∣+∣ ∣ ∣sin A sin Pcos(AQ)cos(AR)sin B sin Pcos(BQ)cos(BR)sin C sin Pcos(CQ)cos(CR)∣ ∣ ∣
Δ=cos P∣ ∣ ∣cos Acos(AQ)cos(AR)cos Bcos(BQ)cos(BR)cos Ccos(CQ)cos(CR)∣ ∣ ∣+sin P∣ ∣ ∣sin Acos(AQ)cos(AR)sin Bcos(BQ)cos(BR)sin Ccos(CQ)cos(CR)∣ ∣ ∣
Applying C2C2C1 cos Q, C3C3C1 cos R in first determinant and C2C2C1 sin Q and in second determinant
Δ=cos P∣ ∣cos Asin A sin Qsin A sin Rcos Bsin B sin Qsin B sin Rcos Csin C sin Qsin C sin R∣ ∣+sin P∣ ∣sin Acos A cos Qcos A cos Rsin Bcos B cos Qcos B cos Rsin Ccos C cos Qcos C cos R∣ ∣Δ=cos P sin Q sin R∣ ∣cos Asin Asin Acos Bsin Bsin Bcos Csin Csin C∣ ∣+sin P cos Q cos R∣ ∣sin Acos Acos Asin Bcos Bcos Bsin Ccos Ccos C∣ ∣
Δ = 0 + 0 = 0

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image